Dr Diarmuid Martin told RTE that the Church had to be very careful that this was not done in the forthcoming debate on the same-sex referendum in the Republic.
Archbishop Martin said he felt that the debate had already got off to a bad start.
Discussions have to be carried out in a "mature" way so that people can freely express their views, while at the same time being respectful and not causing offence, he said.
He said Church teaching was that marriage was between a man and a woman, exclusively, but that this approach did not exclude gay people from celebrating their union by a different means.
Responding to Dr Martin's comments, the Gay and Lesbian Equality Network said they are disappointed by the comments made by the Archbishop of Dublin regarding same sex marriage and homophobia.
GLEN’s Brian Sheehan described it as “a missed opportunity” to tackle the role of the church and church teachings in creating what it said were “some of the difficult realities for lesbian and gay people in Ireland today”.
However, he welcomed Dr Martin’s acknowledgement of the impact that a culture, which still has homophobia as part of it, has on those who are lesbian, gay, bisexual and transgender.
Meanwhile, Taoiseach Enda Kenny called for a rational, calm and considered debate ahead of a referendum on same sex marriage next year.
Also speaking on RTÉ's This week, Mr Kenny said he never considered legislating for same-sex marriage and that it was instead an issue for a referendum.
He also promised to partake in the discussion in the lead-up to the referendum.
Mr Kenny said the Government deemed it important for people to have a debate before they vote in the impending referendum.
“We believe that it's important the people have a rational, common-sense. calm, considered and compassionate debate about this and I hope that happens.
“Next year people will make their decisions. I didn't consider legislating for this, it is a question for a referendum and it will be held next year,” said Mr Kenny.