Answer
Salam Dear Nadia,
Thank you for your question and for contacting Ask About Islam.
Marriage in Islam is a highly regarded practice in the prophetic example, as well as being a social necessity. The Prophet (peace be upon him) said:
‘O you young men! Whoever is able to marry should marry, for that will help him to lower his gaze and guard his modesty.’
Actually the Prophet (peace be upon him) regarded modesty as a great virtue. He said:
‘Modesty is part of faith.’
He also said:
‘Marriage is my Sunnah (way and example). Whosoever keeps away from it is not from me.’
Also, socially, marriage is necessary in Islam. This is because through marriage, families, which are the fundamental unit of the society, are established. Through marriage, Islam aims to build a pure, safe, clean, healthy, and socially stable society.
Therefore, mutual respect, common ground and shared principles, are highly needed from both parties. This is in order to fulfill both the religious purpose and the social necessity. In addition to all of this, marriage in Islam is established on the basis of mutual consent and free choice.
Since marriage is highly regarded by religion, Islam considers believing in the existence of God, the institution of prophet-hood and the divine books as essential elements in its foundation. Thus Allah in the Noble Quran made clear that marrying disbelievers is prohibited, for both genders:
{Do not marry unbelieving women (idolaters), until they believe: A slave woman who believes is better than an unbelieving woman, even though she allures you. Nor marry (your girls) to unbelievers until they believe: A man slave who believes is better than an unbeliever, even though he allures you. Unbelievers do (but) beckon you to the Fire. But God beckons by His Grace to the Garden (of bliss) and forgiveness, and makes His Signs clear to mankind: That they may celebrate His praise.}
Surah 2 Verse 221
However, in contrast with other faiths, Islam did not restrict marriage to be only within the Islamic faith. Islam did not require conversion into the faith as a condition for the interfaith marriage, like Christianity. Nor did it totally reject the idea of interfaith marriages, as in Judaism. Here, I am referring to the scriptural law of Christianity and Judaism, not to the civil laws of Western countries.
Simultaneously, Islam is a religion that is suitable for the innate nature and character of the human being. In order to maintain security, order and purity in the society, Islam seeks to maintain qualities within the foundation of the family. In this sense only, Islam considers the husband to be the head of the family and responsible for the well being of family members.
It is a matter of fact that a Muslim man is obliged to recognize and respect the faith of the Christian and the Jewish woman and cannot compel her to become Mu
slim. On the other hand, the same cannot be said of the non-Muslim man.
The faith of any non-Muslim man does not even recognize Islam or Prophet Muhammad (peace be upon him) as being legitimate. He would not necessarily respect Islam’s tenets and practices that a Muslim woman obviously believes in and is obliged to uphold.
Thus the rights of Christian and Jewish women in a Muslim household are protected in the Islamic law. They are able to practice their religion freely without any restriction and they can live with the knowledge that their Prophets and Books will be honored. A Muslim man is even commanded to believe that it is an article of faith to treat his Jewish or Christian wife in this way.
Additionally, the habits of the non-Muslim husband and his morals will likely be in conflict with and compromise those of the Muslim woman. Contrary to this, the morals and the value system of the Muslim husband, if not identical to the principle values of Christianity and Judaism, will not contradict or threaten them.
Hence, under the light of all previous facts, allowing Muslim men to marry non-Muslims and the prohibition for Muslim women to do so is not a discriminatory rule. It is not a threat to the equality of men and women, or an indication of the dominance of man. It is directly related to respecting others faiths and the freedom of religions.
Salam
Mr. Lamaan Ball, former editor of Ask About Islam, adds:
In order to be clear, we need to understand how the rights to practice your religion are affected by marriage. If both parties were equal partners with neither being able to impose his or her will upon the other, then Muslim women marrying Christian or Jewish men would be no different to the Muslim men marrying Christian or Jewish women. However there is a difference. Christian and Jewish men are clearly set in charge of their wives and have a right to be obeyed by them.
Christian marriage vows include obeying the husband. The bible explicitly curses Eve by saying she will be made to obey men (This 
story is however completely missing in the Quran). It has even been until recently (early last century) the law in England, that upon marriage all of the woman’s property becomes the property of her husband. So any control she had over her life is surrendered to her husband.
Islam recognizes the position of difficulty this could land Muslim women in and so does not allow them to be subjected to the orders of Christian or Jewish husbands.
Salam and please keep in touch.