At the most fundamental level, a gay marriage is impossible because the same-sex couple can never consummate their marriage; they can never become one flesh (or unify). Also, the combination of their sexual organs can never produce children; they only have half the parts necessary but doubled.
It is not to say that gay people are incapable of loving each other in the same fashion as anyone else or that they cannot care for their partner and stay as committed as anyone else if not better. A homosexual union is intrinsically impossible because they cannot unify.
Sexual intercourse is the sign of marriage and the act of sexual intercourse is the renewal of the covenant of marriage so two same-sex people can never complete their marriage.
For this reason it is intrinsically impossible for two people of the same sex to marry. It is not discriminatory, it is not homophobia, and it is not
hatred of gay people. The marital act can simply never occur between two people of the same gender.
This is not to say that homosexual people are any less of a person than heterosexuals. All people, regardless of age, color, race, sexual orientation, religion, etc. are equal in dignity.
As a member of God’s creation each person should be given the due respect that a person deserves because in the eyes of the Lord we are not separated by age, color, race, or sexual orientation (Cf. Gal. 3:28). Each person may not be equal in all abilities, but we are equal in dignity.