Single Muslim men can marry a non Muslim Women however, Muslim Women cannot perform Shaadi with a Non Muslim man, so I guess the next question is why is it permissible for a Single Muslim man to marry a Christian or a Jewish woman, and at the same time, it is forbidden that a Muslim woman? Shaadi for a Muslim man to a Jewish or a Christian woman, is an exceptional rule however only applied under special circumstances.
Shaadi for a Muslim man to a Jewish or a Christian woman, there is no problem, because he believes in all the prophets, and holy books.
Islam teaches, or should I say commands him to be fair with his wife regardless of her faith (Christian or Jewish).
Shaadi for a Muslim man who decides to go ahead in marriage with a lady of the Christian or Jewish faith, he must have a strong belief in his faith, and should also strongly abide by his religion.
Single Muslim men can only marry in to Christianity and Judaism (and obviously Islam) and aren't permissible to marry a Magian (Zoroastrian) woman, communist woman or an idol-worshipper The simplest reason forbidding a Single Muslim woman from performing Shaadi with a non-Muslim is that he (Christian or Jewish) only believes in his prophets, and doesn't believe in the prophet Mohamed (pbuh) or any of the other prophets (blessing be upon them).
Shaadi with a non Muslim husband will cause problems, especially in the up-brining of the kids, let me give you an example, when say the Muslim woman tries to teach the kids to love and respect all prophets (including Muhammad pbuh) and believe in all of them, the non-Muslim husband will object, he has different beliefs when it comes to prophets...
He will disagree and cause problems in the way she raises the kids, preventing her from raising them in an Islamic way, and here comes the real problem, she'll have two options, either she leaves the whole thing as it is and accepts that the kids will not be raised with entire Islamic beliefs or she argues the matter, causing problems in the marriage, possibly ending in divorce.
On the other hand, no such problems will occur between a Muslim husband, and a non Muslim wife.
If the wife wants to teach the kids to love and believe in her prophet/s, the Muslim husband will not refuse, the reason being is quite simple, he also believes in the same prophets.
This is one of the reasons why Islam allows the marriage between Muslim man to a Jewish or a Christian woman, and forbids the marriage between Muslim woman, and non-Muslim man.
In Islam you are taught to respect the marital relationship and there is a need to want to guarantee its stability.
Finally, I would like to mention that when performing Shaadi with a Women of the faith Christianity or Judaism, she must be of the old and original testament.
In modern Christianity and some Judaism sects homosexually and the consumption of Alcohol amongst other things is accepted.
It is the duty of the Muslim Male to insure research is done before committing to holy matrimony.