سم الله الرحمن الرحيم
Bismillā hir Rahmā nir Rahīm
In the name of Allah, Most Gracious, Most Merciful
As-Salāmu `Alaykum (السلام عليكم):
This question is asked to the Muslims who actually have married non-Muslim or Non-Kitab (Who have no understanding or observe shirk-joining partners with Allah). No need to assume why. Asking the Muslims who have married non-Muslims why.
(You can answer anonymously)
This question can't be answered with opinions, by one who hasn't married a non-Muslim, or isn't married.
(Please reread)
Surah Al-Mai'dah 5:5
Made lawful to you this day are At*Tayyibât [all kinds of Halâl (lawful) foods, which Allâh has made lawful (meat of slaughtered eatable animals, etc., milk products, fats, vegetables and fruits, etc.). The food (slaughtered cattle, eatable animals, etc.) of the people of the Scripture (Jews and Christians) is lawful to you and yours is lawful to them. (Lawful to you in marriage) are chaste women from the believers and chaste women from those who were given the Scripture (Jews and Christians)
before your time, when you have given their due Mahr (bridal money given by the husband to his wife at the time of marriage), desiring chastity (i.e. taking them in legal wedlock) not committing illegal sexual intercourse, nor taking them as girl-friends. And whosoever disbelieves in the Oneness of Allâh and in all the other Articles of Faith [i.e. His (Allâh's), Angels, His Holy Books, His Messengers, the Day of Resurrection and Al*Qadar (Divine Preordainments)], then fruitless is his work, and in the Hereafter he will be among the losers.
(translation by: Dr. Muhammad Muhsin Khan)
Before your time!
Dr. Yusuf Al-Qaradhawi on marrying non-Muslims:
http://www.islamfortoday.com/interfaithmarriage.htm