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 tranquility, 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).
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.
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.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?
Islam is consistent with itself in prohibiting the Muslim man to marry a mushrik (polytheist) woman(for example Hindu), 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."
Another point to be stressed here is that, Islam does not force anyone to convert to Islam. There is no compulsion in religion.
May Allah guide all of us through the right path.