Why can't a Muslim woman marry a non Muslim man?
Muslim women and men can not marry idolaters. An idolater is the one who assigns partners to Allah, for example who worships idols, stars, fire or animals.
Allah says: O you who believe! Do not marry idolaters unless they believe (1)
There is no drawback for a Muslim man to marry a Jewish or Christian woman. The Islamic scholars agree on this subject. It is written in the verse of Quran that: (Lawful unto you in marriage) are (not only) chaste women who are believers, but chaste women among the People of the Book, revealed before your time,- when ye give them their due dowers, and desire chastity, not lewdness, nor secret intrigues. (2)
The wisdom in the allowance of a marriage with a woman who is one of the followers of the previous scripture is the possibility of this woman to become a believer of Allah, the prophets and the hereafter because of getting married with a Muslim man.
It is forbidden for a Muslim woman to get married with an infidel (unbeliever) man. Nor shall you give your daughters in marriage to idolatrous men, unless they believe. (3)
Because, in such a marriage, there is the danger for the believing woman to fall down to unbelief. The husband may invite his wife to his religion. Women usually obey their husbands and are impressed by their actions and encourage them in their religions. (4)
It is not possible to say that a Muslim girl is allowed to marry a Christian man due to the fact that a Muslim man is permitted to get married with a Christian woman. Because this kind of comprehension means that the serious difference between these two hasnt been recognized. Thus:
A Muslim man who marries a Christian woman doesnt deny the Scripture and the prophet of his Christian wife, on the contrary he approves them and he never disrespects to them. So, a Christian woman isnt subjected to despise and disrespect by her Muslim husband because of her religion. So, there is no losing of anything for her. However, a Christian man that a Muslim girl marries doesnt possess such an approval and respect. A Christian man is moderated to accept neither Hadhrat Mohammad (PBUH) nor Quran that the Muslim girl believes in. So, a Muslim girl is subjected to despise by getting under the wedlock of a man denying her Scripture, prophet and religion. The obstacle of this marriage is because of this despising. The only solution for such a marriage is that, like a Muslim man, the Christian man must accept the Scripture and the prophet of the Muslim woman whom he wants to get marry with by disclosing his belief through the phrase of the Islamic testimony (I testify that there is no god but Allah, and I testify that Muhammad is Allahs Messenger). Thus, like a Christian woman, a Muslim woman will attain the equality of getting married someone that doesnt deny her religion and the subject will be solved in a fair way.
This means that, none of the women must direct herself in a position that she is obliged to marry a man that despises her by denying her scripture and her prophet. Because that forces her to an invalid marriage.
The explanations in the verse Al- Baqarah, 221 and in the verse Al-Ma'edah, 5 can be referred.
If a Christian man embraces Islam, then a Muslim woman is allowed to marry him.
(1) Al- Baqarah, 221
(2) Al-Ma'edah, 5
(3) Al- Baqarah, 221
(4) Fetevâ-i Hindiye 11/330