Wife Wants to Leave But He Doesn’t Want to Divorce Her
Question

                My wife refuses to have sexual relations for last 3 months, does not let me touch her, says I am fat and ugly, wants to separate and is forcing me to say that we should separate.

I do not want to let her go , I love her very much, But I just dont know what to do?
Praise be to Allah.
    Firstly: 

    It is not permissible for the woman to refuse to go to bed 
    with her husband without a valid excuse such as menses, sickness or an 
    obligatory duty such as fasting, Hajj and the like. If she does that then 
    she has exposed herself to sin and curses. It was narrated that Abu Hurayrah 
    (may Allah be pleased with him) said: The Messenger of Allah (blessings and 
    peace of Allah be upon him) said: “If a man calls his wife to his bed and 
    she refuses, and he goes to sleep angry with her, the angels will curse her 
    until morning comes.”

    Narrated by al-Bukhaari, 2998. 

    And it was narrated that Abu Hurayrah said: The Prophet 
    (blessings and peace of Allah be upon him) said: “If a woman stays away from 
    her husband’s bed, the angels will curse her until she comes back.”

    Narrated by al-Bukhaari, 4795. 

    Based on that, what your wife is doing of refusing to come to your bed is a haram (impermissible) action; in fact it is a major sin and is nushooz (wilful defiance) because of which her right to maintenance and a fair share 
    of your time (in the event of plural marriage) is waived. 

    It says in al-Haawi al-Kabeer by al-Mawardi (11/438): 
    There are two conditions that the woman must meet in order to be entitled to 
    maintenance:

    1.Allowing him to be intimate 
    with her

    2.Agreeing to move with him 
    wherever he wants in the city in which he married her or to any other city, 
    if the roads are safe.

    If she allows him to be intimate with her but does not agree 
    to move with him, then he is not obliged to spend on her maintenance. 

    If she responds to him with regard to moving but does not 
    allow him to be intimate with her, if that is for a reason that makes intimacy haraam, such as menses, ihram (ritual state one is in for the pilgrimage)and fasting, then her right to maintenance is not waived, because it is forbidden for him according to sharee‘ah (Islamic law), so it is an exemption from what is required in the marriage 
    contract. But if her refusal is for no good reason, then her right to 
    maintenance is waived, if intimacy was possible. End quote. 

    Secondly: 

    If the wife does not want to stay with her husband and it is 
    not possible for them to live together, and she thinks that she will never 
    be able to fulfil the rights he has over her, then Islam gives her a way out 
    and relief from this situation that is unbearable for her, as she cannot 
    bear to live with him and she is unable to fulfil the rights he has over 
    her. So Islam allows her to separate from him by means of khula‘. 

    Al-Bukhaari (4867) narrated from Ibn ‘Abbaas (may Allah be 
    pleased with him) that the wife of Thaabit ibn Qays came to the Prophet 
    (peace and blessings of Allaah be upon him) and said: “O Messenger of Allaah, I do not blame Thaabit ibn Qays for any defect in his character or his religious commitment, but I would hate to commit an act of kufr (disbelief) when I am a Muslim.”  The Messenger of Allaah (peace and blessings of Allaah be 
    upon him) said, “Will you give him back his garden [which he had given as mahr/dowry]?” She said, “Yes.” The Messenger of Allaah (peace and blessings of 
    Allaah be upon him) said (to Thaabit), “Accept the garden, and divorce her 
    once.”  

    See also the answer to questions no.
    1859 and
    91878 

    Thirdly: 

    Our advice to you is: so long as your wife is asking you for 
    a divorce and does not want to stay with you, then you should divorce her, 
    because there is no interest for a man in staying with a wife who does not 
    love him and does not obey him in what he wants from her or give him the 
    least of the rights he has over her. 

    As for your love for her, there will be no joy for you in 
    that so long as she does not reciprocate in kind. You should ask Allah to 
    bless you with another wife whom you love and who loves you. 

    In this case it is permissible for you to refuse to divorce 
    her until she ransoms herself from you with some money or wealth. This is 
    the khula‘ which we mentioned above. In his commentary on the verse in which 
    Allah says (interpretation of the meaning): “Nor should ye treat them with harshness, that ye may take away part of the dower ye have given 
    them,-except where they have been guilty of open lewdness” [an-Nisa’ 4:19], 
    Ibn Katheer said: Ibn Mas‘ood and Ibn ‘Abbaas said: What is meant thereby is zina, i.e., if she commits zina (adultery), then you have the right to take back from her the mahr you gave her and to put pressure on her until she gives back the mahr, then divorce her through khula‘. 

    Ibn ‘Abbaas, ‘Ikrimah and ad-Dahhaak said: “open lewdness” 
    refers to wilful defiance and disobedience. 

    Ibn Jareer favoured the view that it includes all of that: 
    zina, disobedience, wilful defiance, a sharp tongue and so on. In other 
    words, all of that makes it permissible to put pressure on her until she 
    gives him his dues or some of it, or he leaves her. And this is good.

    End quote from Tafseer at-Tabari, 8/115-118 

    We ask Allah to make things easy for you and to guide you and 
    help you to do that in which is good. 

    And Allah knows best.