First of all, it is to be stressed that Islam does not encourage the interfaith marriages. The general rule of Islam is that Muslims should marry Muslims. A Muslim male or female should not marry a non-Muslim male or female. The only exception is given to Muslim men who are allowed to marry the chaste girls from among the People of the Book.
However, a Muslim woman is better suited to a Muslim man than a woman of Christian or Jewish faith, regardless of her merits. This is because marriage is not based on fulfilling one’s sexual desires; rather, it is an institution. It aims to establish a home on the bases of tranquillity, faith and Islamic morals. To fulfil this task, the whole family must apply Allah’s course and try to convey His message.
It is obvious that Islam made it impermissible for a Muslim woman to marry a non-Muslim with aim of keeping her away from things that may jeopardize her faith. In fact, Islam aims at protecting religion. To achieve this goal, it prohibits a Muslim from being involved in something that represents a threat to his religion. A Muslim woman will not feel that her religion is secure while being with a Jewish or a Christian husband especially as the majority of the People of the Book do not show due respect to our Prophet, Muhammad (peace and blessings be upon him).
Allah Almighty says: “And the Jews will not be pleased with thee, nor will the Christians, till thou follow their creed. Say: Lo! The guidance of Allah (Himself) is Guidance. And if thou shouldst follow their desires after the knowledge which hath come unto thee, then wouldst thou have from Allah no protecting friend nor helper.” (Al-Baqarah: 120)
Given the fact that the husband is generally the head of the household, it’s not far-fetched for a non-Muslim husband to prevent his Muslim wife from performing some Islamic rituals which may seem a nuisance to him, for example fasting, or even refraining from marital relations during the fast. As a result, he might force her to change her religion, and if she refuses, the situation may culminate in divorce.
as for why Islam allows a Muslim man to marry a Christian or Jewish woman, it’s clear that every Muslim believes in Moses and Jesus (peace be upon them) and he holds all the Prophets of Allah in high esteem. Thus a Muslim finds no harm in his wife’s being a Christian or a Jew, for the spirit of tolerance Islam holds for other religions is ingrained in him.
The eminent Muslim scholar, Sheik Yusuf Al-Qaradawi, in his well-known book, The Lawful and the Prohibited in Islam, stated that: “It is haram for a Muslim woman to marry a non-Muslim man, regardless of whether he is of the People of the Book or not. We have already mentioned the saying of Allah, “…and do not marry (your girls) to idolaters until they believe…” (Al-Baqarah: 221)

And He said concerning the immigrant Muslim women: “Then if you know them to be Believers, do not send them back to the unbelievers. They are not lawful for them (as wives), nor are they lawful for them (as husbands).” (Al-Mumtahanah: 10)
No text exists which makes exceptions for the People of the Book. Hence, on the basis of the above verses, there is a consensus among Muslims concerning this prohibition.
thus, while a Muslim man is permitted to marry a Christian or Jewish woman, a Muslim woman is not allowed to marry a Christian or Jewish man. There are many sound reasons for this difference. First, the man is the head of the household, the one who maintains the family, and he is responsible for his wife. And while Islam guarantees freedom of belief and practice to the Christian or Jewish wife of a Muslim, safeguarding her rights according to her own faith, other religions, such as Judaism and Christianity, do not guarantee the wife of a different faith freedom of belief and practice, nor do they safeguard her rights. Since this is the case, how can Islam take chances on the future of its daughters by giving them into the hands of people who neither honor their religion nor are concerned to protect their rights?
a marriage between a man and woman of different faiths can be based only on the husband’s respect for his wife’s beliefs; otherwise a good relationship can never develop. Now, the Muslim believes that both Judaism and Christianity originated in divine revelation, although later distortions were introduced into them. He also believes that God revealed the Tawrah to Moses and the Injeel to Jesus, and that both Moses and Jesus (peace be on them) were among the Messengers of Allah who were distinguished by their steadfast determination. Accordingly, the Christian or Jewish wife of a Muslim lives under the protection of a man who respects the basic tenets of her faith, her Scripture, and her Prophets, while in contrast to this the Jew or Christian recognizes neither the Divine origin of Islam, its Book, or its Prophet (peace be on him). How then could a Muslim woman live with such a man, while her religion requires of her the observance of certain worships, duties, and obligations, as well as certain prohibitions. It would be impossible for the Muslim woman to retain her respect for her beliefs as well as to practice her religion properly if she were opposed in this regard by the master of the house at every step.
It will be realized from this that Islam is consistent with itself in prohibiting the Muslim man to marry a mushrik (polytheist) woman, for since Islam is absolutely opposed to shirk (polytheism), it would obviously be impossible for two such people to live together in harmony and love.”