I wanted to know do Islamic teachings allow a Muslim to marry a Hindu girl? If so then what is the reason of this permission and if does not then why?
Faith and religion is a very important matter for all the individuals. Therefore, commonly people marry into their respective faiths. However, the Islamic Shari'ah has allowed Muslims to marry women of the People of the Book. This it should be noted is also a conditional allowance. The Holy Qur'an only allowed the Muslims to marry into adherents of these faiths when the supremacy of Islam was established in the Arabian Peninsula. The People of the Book were living the life of subjugation. The Holy Qur'an made subtle allusion to the fact. The related verse of the Holy Qur'an reads:
The Qur'anic words 'now you can marry' clearly allude to the fact that the circumstances and position of Muslims is considered in this regard. We cannot marry in any circumstances among the followers of other religious barring the People of the Book.
This day are [all] good things made lawful for you. The food of those who have received the Scripture is lawful for you, and your food is lawful for them. And so are the virtuous women of the believers and the virtuous women of those who received the Scripture before you (lawful for you) when ye give them their marriage portions and live with them in honor, not in fornication, nor taking them as secret concubines. Whoso denies the faith, his work is vain and he will be among the losers in the Hereafter. (5:5)