She thinks that Islam is not suited to the modern woman
Question

There is a girl in my locality, who holds following beliefes
1. Women are more active and sometimes superior to man. 
2. Man can't live without woman and want her body. Do, she hates all men. 
3. She wears hijab and says it empowers her and gives her freedom from against the "dominance" of man. 
4. She supports secularism and says a hijabi can gain her rights through a secular tradition than living under a islamic society. 
5. She distorts the idea of jihad and says there's no jihad in this age. 
6. Once she was told how she views cooking, she replied that cooking is for man and it's not the job of woman. 
7. She says she's proud to be a muslim and says shes struggling to establish "modern islam" So, shaykh what advice I can give to her as she's my classmate?
Praise be to Allah.Firstly:
There are some positive aspects to this girl which we must point out. Her pride in Islam is something praiseworthy, as is her keenness to belong to Islam, her admiration of its values, and her commitment to its teachings, such as the hijab for example, whether she calls it modern Islam or some other name. It does not matter what she calls it if she can understand the concept behind that name in a proper manner, far removed from the influence of emotions that young people usually feel, and far away from extreme ideas that result from the crisis that the Muslim ummah is going through in reaction to the domination of modernity.
Secondly:
There is a difference in approach between talking to an older woman who has gone through a lot of life experiences, and has read, heard and researched things, until she formed a certain conviction that what she believes is sound and it is very difficult for her to change her views – rather she strives to defend them –
and talking to a young girl of sixteen, who does not have enough knowledge, education or life experience to her credit; rather she is still at the stage of growth and development, and has not yet reached the age of maturity and her ideas are not yet fully formed, and she has formed whatever ideas she has on the basis of limited experience, or merely listening to one experience of someone else, or imitating a particular person.
Such ideas and thoughts that accumulate and dominate the mind of a person when he is physically and intellectually immature will quickly change, the more intellectually mature the person becomes and the more he goes through life experiences and increases in knowledge.
Based on that: it is important to differentiate between the ideas of this young woman, some of which are acceptable and some are to be rejected or, more precisely, between general ideas that have nothing to do with religious principles – rather they are personal impressions that are subject to change as the person gains more experience – and religious concepts or beliefs which could have an impact on the fundamentals of religion.
Her idea that women are superior in terms of energy and hard work, and her dislike of the idea that there is natural attraction between the sexes, and her suggesting that men should participate in cooking and preparation of food, are all matters that do not reach the level of beliefs or doctrines, as you mentioned at the beginning of your question. That is because they are no more than passing thoughts and personal desires that she chooses for herself and her evaluation of some permissible deeds. There is nothing wrong with her thinking about the women around her as being more active, working harder and serving others in a manner that is superior to what she sees from the men, whether they are other female students who outperform the male students – which is something that happens often – or she sees that among some outstanding women around her. That could very well be the case, and there is no doubt about it, but to be fair, we should note that women surpassing men is something rare, because if we look at men and women together as a whole, we will see that men do surpass women with regard to working hard and being active and energetic. The reality of people’s lives attests to that.
Look at all nations of the world, advanced or otherwise: how many female presidents are there, how many female prime ministers, how many female ministers, how many female CEOs of large corporations or major companies, and so on?
You will undoubtedly find some women in such positions, but they are very few when compared with the number of men in such positions.
This fact is an affirmation that you will find in all peoples in the world, despite the differences in their religions and cultures. This confirms that men are more capable than women of successfully performing in these high positions, and that is the natural disposition that Allah has instilled in people.
Also look at inventors, explorers, scholars and scientists throughout all of human history, which is not limited to the Muslims alone; what is the ratio of women to men?
Undoubtedly it is very small, and women in such roles are rare.
Women who are superior to some men do exist, and that cannot be denied, but their numbers are very few. This idea, in this sense, is not contrary to Islam at all. Some of the scholars have clearly stated that.
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said:
If you say: “Men are better than women,” that does not mean that each individual man is superior to each individual woman. Rather what is meant is that this category in general terms is superior to that category, even though there may be individual women who are superior to some men."(Al-Usul min ‘Ilm al-Usul  p.36).
Something similar was stated in Fawatih al-Rahamut (p. 1/440).
Something similar may be said about her idea that men are interested in women’s bodies, and she hates men because of their gender. We do not think that these are “beliefs”, as you called them at the beginning of your question. They are not beliefs or principles of any significance or any religious dimension. Rather they are only feelings or emotions which your friend is expressing without thinking. The cause of that – as appears to be the case – is some painful experiences that she has lived through, or some unpleasant scenes or experiences that she faced or heard about, which led to her forming these impressions and phobias regarding these matters.
Or perhaps that stems from some inner desire, such as thinking highly of herself or seeking to elevate herself and try to rise above her imagined weaknesses. These are just thoughts and aspirations that many people have, especially at a young age and at the time of adolescence.
All of this is something that may change, or at least is something that is changeable with the first successful or beneficial experience she goes through. Her situation may easily improve with more education in the wider world beyond her narrow surroundings, so she will see the wisdom behind human integration between the male and female genders, which goes beyond the short-lived sexual dimension to an intangible spiritual dimension based on values that result from this integration between the sexes, as the Lord of Glory, may He be glorified and exalted, says (interpretation of the meaning):
{And of His signs is that He created for you from yourselves mates that you may find tranquillity in them; and He placed between you affection and mercy. Indeed in that are signs for a people who give thought} [ar-Rum 30:21].
This mistaken view, even though it is held by some women, is something that we hope will change soon, before it affects the personal life of this young woman and she causes some harm to herself which she will regret when regret will not benefit her.
What will help her to change her point of view – in addition to what we have mentioned above – is noting that the majority of women of different cultures and religions do not think in that way – because it is contrary to human nature. The evidence for that is the fact that the number of married women is always greater than the number of unmarried women; moreover, many of these unmarried women – in fact most of them – are not happy with their situation, and each of them wishes that she was a mother or had a family.
As for her talking about the situation of women in secular countries, the reason for that, in our view, is twofold:
Firstly, it stems from lack of knowledge (ignorance) of the status of women in Islamic teachings, the high esteem in which woman is held in Islam, the recognition of her rights, how Islam protects her dignity and instructs men to treat women kindly and not to mistreat them. Rather she is looking at some Muslim societies which may go against the teachings of Islam and mistreat and oppress women. Islam has nothing to do with that; rather these are mistakes and the responsibility for them rests with the one who does that and he is the one who will be brought to account for it. Such things should not be attributed to Islam.
Secondly: it stems from not looking at the real situation in society in the light of official numbers and precise statistics which describe what women are going through in those secular societies, and from being deceived by some apparent freedoms for women that this girl sees here and there. In this regard, it is sufficient to draw this girl’s attention to the international acknowledgement of incidents of sexual harassment, rape and appalling sexual exploitation, news of which has reached everywhere and people everywhere talk about it, to the extent that there are reports that half of British women have faced sexual harassment of different types, according to the BBC.
If you look, fairly and objectively at the following statistics, you will realize that the matter is more subtle and deeper than may appear at first to be case:
1.. 10.4 million families in America are headed by single mothers who are the sole providers for their families, according to the US Census Bureau.
2.. More than one million children are killed by abortion every year in the United States of America, according to the American government Centers for Disease Control.
3.. 683,000 women annually are subjected to rape in America, at a rate of seventy-eight women per hour, as stated by the American Department of Justice.
4.. 1320 women are killed annually, meaning that approximately four women are killed every day, by their husbands or boyfriends in America.
5.. Approximately three million women every year in America are subject to physical abuse from a husband or boyfriend. Source: the official government website of the State of New Jersey.
6.. 22.1% of women in America are subjected to physical abuse by a husband or boyfriend (current or former), according to the US Department of Justice.
7.. A report issued by the US Bureau of Labor Statistics confirms that most women in the West work in low-wage and low status jobs, and despite the pressure that the government exerts to improve women’s jobs, 97% of higher leadership positions in most companies are occupied by men.
8.. 78% of women in the armed forces are subjected to sexual harassment from military employees.
9.. In America, a woman’s body is a commodity that is traded to the extent that women are treated like animals. The aim of that is mere sexual pleasure, to the extent that some widely known restaurants there serve food on the naked bodies of women, and some car washes offer car washing services done by naked women, and waitresses serve coffee in one of the most famous restaurants wearing bikinis, as was published in major American newspapers such as the New York Times (18-4-2007, 24-8-2008, etc).
10.. Approximately fifty thousand women and girls are trafficked into the United States every year, where they are enslaved and forced into prostitution, according to the New York Times.
11.. Exploitation of women’s bodies in various permissive ways is an industry that brings in twelve billion dollars annually in America alone, according to a report on www.reuters.com
12.. Half of American women above the age of seventy-five years live alone, as noted by the American Census Bureau.
13.. Women were not given the right to vote in America until 1920 CE.
14.. According to a study carried out in fourteen countries, it was shown that 42% of British people admit having illicit relationships with more than one person at the same time, whilst half of Americans have illicit relationships. The rate in Italy is 38% and in France it is 36%, according to the BBC.
There is an almost endless list of dark, hidden pages which speak of the situation of women in materialistic Western civilisation, all of which have been documented on official Western websites which constitute trustworthy and reliable sources for such statistics.
Please see the statistics on www.alukah.net
With regard to her view on jihad, it is a mistaken view, the source of which is ignorance of the rulings on jihad in Islam and the wisdom behind its prescription.
The Prophet (blessings and peace of Allah be upon him) said: “Goodness is tied to the forelocks of horses until the Day of Resurrection: reward and booty.”
Al-Hafiz Ibn Hajar (may Allah have mercy on him) said: The booty that is associated with reward is only acquired by means of fighting on horses in jihad."(Fath al-Bari  6/56).
This hadith clearly indicates that jihad will continue until the Day of Resurrection. On our website there are many questions about the rulings on jihad; please find them under the heading Jihad and Hijrah (migration).
These are some ideas which we believe will help you to advise this girl.
But we recommend you to let your advice to her be simply to tell her to refer to this question, or print it out for her.
As for talking to her, when you are a young man and she is a girl, we think that this is something that could open the door to temptation, so you must close that door and not open it, because it may lead to something that is bad for you and her.
And Allah knows best.