Islam *does *preach equality between man and woman, but does not hold them to be identical. Both are very different.
A Muslim man cannot marry any random Christan/Jewish women - they have to be chaste (“Lawful unto you in marriage… are… chaste women among the People of the Book, revealed before your time…” - Quran 5:5).
An excellent link highlighing some reasons why a marriage between a Muslim woman and a non-Muslim man may not be successful: LINK