Rationality is one of those things that is always relative. You can be anti-marriage equality and quite lovely otherwise, but unless you can come up with a non-religious, backed-up-by-facts reason why my wife and I should not be allowed to get the legal benefits assigned without question to drug addicts, child abusers, grifters, murderers, and politicians who happen to be in heterosexual relationships, you have no "rational" basis for your position.
This is the crux of the matter. You are welcome to be against marriage equality, but chances are you have one of several reasons for your feelings and none of them are actually rational. The definition of marriage has changed many times over the years. It's not rational to believe it has not. In my lifetime it has changed, when interracial marriages were made legal federally. So there is no rationality in insisting that the definition has not changed for hundreds (much less thousands) of years. It's irrational to rely on the Bible as a guide, since men had multiple wives and slept with slaves in the pages of those books.
So, what rational basis for not supporting marriage equality exists? Let's take a look at some of the most common arguments.
Children are *not* why people get married 100 percent of the time, so obsessing about them is not rational. We allow infertile heterosexual couples to gain the benefits of marriage. Almost every study has pointed to the fact that children raised by same-sex couples are perfectly fine. The one study that is flogged as contradicting this has been retracted by the journal that published it and repudiated by every major medical organization.
The country will gain more taxes if you allow me to marry. So it will be a net benefit to the bottom line. Private sector has already acknowledged that benefits for families of any kind is good for business.
That leaves the fact that it just bugs the hell out of you. The world is changing and you do not like it. That's a valid reason, and a human one, but you know ... it's not rational.
When you have a truly rational reason, that is not based in fear, loathing, selfishness, pride, anger, or lust, then sure, we'll consider it something other than homophobia.
More questions on same-sex marriage: