Dr John Sentamu was challenged on the issues during a heated interview with broadcaster Piers Morgan on ITV's Good Morning Britain programme.
"You can still have your view, in terms of teaching the church's position on marriage, and, at the same time, be intolerant of those who are homophobic," the senior clergyman argued.
He said: "The church's teaching on marriage between a man and a woman is very clear. I support civil partnerships because for me that's a matter of equality, a matter of fairness.
"My upholding of Christian marriage, as I understand it, goes hand and hand with saying to people that to diminish homosexual people is anathema to the Christian faith because God loves us all equally."
Morgan quizzed Archbishop John on the Church's attitude towards gay people, "Is homosexuality a sin?" He asked.
"I would never say that," the archbishop replied, "I will never say that because sin is doing something consciously against God."
The interview comes just days after 49 people were massacred in a homophobic terrorist attack at an LGBT club in the United States.
Morgan said: "You've taken a pretty strong stance against gay marriage. Is it about time that religious leaders from all faiths came together and were more tolerant generally towards homosexuality?"
The archbishop told him the Church was clear that homophobia was wrong: "I've got a lot of gay friends and they see me as a friend, as someone who wants to support and defend them against homophobia.
"Not supporting gay marriage does not equal homophobia."
Archbishop John angrily dismissed suggestions homophobia and the persecution of the LGBT community was akin to racism: "This is the trouble I have with the people who argue that the question of sexuality is equal in terms of argument to the question of slavery.
"No, some of my relations died on the ships. Slavery was a very wrong thing."