A Christian woman is saying: Why is it not permissible for a Muslim woman to marry a kitaabi man when the opposite is permitted?
Question

My Christian wife is asking: Why is it not permissible for a Muslim woman to marry someone from among the people of the Book – Christians and Jews – whilst that is permitted to Muslim men?.
Praise be to Allah.One of the names of Allah in which we believe – and we do not think that anyone who believes that he has a Lord will doubt that – is al-Hakeem (the All-Wise). In this manner the noble angels praised Him, because they understood His wisdom in His command to them to prostrate to Adam: 
“They (angels) said: ‘Glory is to You, we have no knowledge except what you have taught us. Verily, it is You, the All-Knower, the All-Wise’” [al-Baqarah 2:32]
He has also testified to this, as have His angels and the people of knowledge: 
“Allah bears witness that Laa ilaaha illa Huwa (none has the right to be worshipped but He), and the angels, and those having knowledge (also give this witness); (He always) maintains His creation in justice. Laa ilaaha illa Huwa (none has the right to be worshipped but He), the All‑Mighty, the All-Wise” [Aal ‘Imraan 3:18]
Thus He has established proof against His creation, as He says (interpretation of the meaning): 
“Say: ‘With Allah is the perfect proof and argument, (i.e. the Oneness of Allah, the sending of His Messengers and His Holy Books, to mankind); had He so willed, He would indeed have guided you all’” [al-An’aam 6:149]
Thus it is known that the All-Wise does not do anything in vain, and He does not do anything that is inappropriate. He does not issue any command but that which is better for His creation than any other, as Allah says (interpretation of the meaning): 
“Allah has sent down the Best Statement, a Book (this Qur’aan), its parts resembling each other (in goodness and truth) (and) oft‑repeated. The skins of those who fear their Lord shiver from it (when they recite it or hear it). Then their skin and their heart soften to the remembrance of Allah. That is the Guidance of Allah. He guides therewith whom He wills; and whomever Allah sends astray, for him there is no guide” [al-Zumar 39:23]
Just as this is implied by His being All-Wise, it is also implied by His being the only Creator. The one who makes a thing knows best what is suited for it, so how about the All-Knowing Creator? 
“Should not He Who has created know? And He is the Most Kind and Courteous (to His slaves), All‑Aware (of everything)” [al-Mulk 67:14]
With regard to the wisdom behind the matter that you are asking about, perhaps you know that Islam is the last religion that was revealed from Allah, hence it abrogates all other religions, as Allah says (interpretation of the meaning): 
“It is He Who has sent His Messenger (Muhammad) with guidance and the religion of truth (Islam), to make it superior over all religions even though the Mushrikoon (polytheists, pagans, idolaters, disbelievers in the Oneness of Allah) hate (it)” [al-Tawbah 9:33]
“And never will Allah grant to the disbelievers a way (to triumph) over the believers” [al-Nisa’ 4:141]
The Messenger of Allah (peace and blessings of Allah be upon him) said; “Islam prevails and is not prevailed over.” Narrated by al-Daaraqutni and others; classed as hasan by al-Albaani in Saheeh al-Jaami’ (2778).  
It is well known that the husband is in charge of his wife (qawaamah) and his status within the family is higher than that of his wife. Perhaps this higher position may make him force his wife to leave her religion and follow his, or it may influence her to do that, and this is something that Islam cannot accept. 
The higher status held by the husband may also cause the children of this woman to follow their father’s religion, which is a great error, if these offspring grow up and do not follow the final religion of Allah. 
This is the important reason which Allah mentioned when He forbade Muslim women to marry non-Muslim men. Allah says (interpretation of the meaning): 
“And give not (your daughters) in marriage to Al‑Mushrikoon till they believe (in Allah Alone) and verily, a believing slave is better than a (free) Mushrik (idolater), even though he pleases you. Those (Al-Mushrikoon) invite you to the Fire, but Allah invites (you) to Paradise and forgiveness by His Leave, and makes His Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) clear to mankind that they may remember” al-Baqarah 2:221]
Moreover, if a kitaabi woman (a Jewish or Christian woman) marries a Muslim man, she is marrying someone who believes in her Prophet and all the Prophets of Allah, because he cannot be a Muslim otherwise, and it is not permissible for him to differentiate between them. Allah says (interpretation of the meaning): 
“The Messenger (Muhammad) believes in what has been sent down to him from his Lord, and (so do) the believers. Each one believes in Allah, His Angels, His Books, and His Messengers. (They say,) ‘We make no distinction between one another of His Messengers’” [al-Baqarah 2:285]
Whereas the kitaabi – whether Jewish or Christian – does not believe in Muhammad (peace and blessings of Allah be upon him) or that he is the Seal of the Prophets, so how can the two matters be equal, and how can Muslim women marry men who do not believe in their Prophet? 
But we should point out here that although it is permissible for a Muslim man to marry a kitaabi woman, because of the interests that it is hoped may be served by that, and to avoid burdening people with too many restrictions, it is blameworthy, as Imam Maalik (may Allah have mercy on him) said. (Tafseer al-Qurtubi, 3/67). 
This permission serves as a hint to the people of the Book, so that they might realize that Islam has made exceptions for the people of the Book in some rulings that it has not made for other kuffaar. Allah has permitted us to eat meat slaughtered by the people of the Book, and He has permitted us to marry their women out of respect for the origin of their religions which were based on Tawheed, and out of respect for the Messengers of those religions in whom we are commanded to believe and respect, and to demonstrate the difference between the attitude of the followers of Judaism and Christianity towards our Prophet Muhammad (peace and blessings of Allah be upon him) and the attitude of our religion towards their Prophets.  
Finally, this ruling should not be strange for other religions, and it is not something odd that is applied by Islam alone. Why should some of those who attack our religion find it strange that Islam forbids our women to marry non-Muslim men, when they do not marry one another even though they are followers of one religion? A Catholic cannot marry a Protestant woman and if he does so he is punished by the church, and vice versa.  
According to the canon of the Egyptian Orthodox Coptic Church published in 1938 CE, article 6 states that “difference in religion is an impediment to marriage.” 
And Allah knows best.