Homosexuals have EXACTLY the same rights I do. Any man can marry any woman who is willing. Just as I can.
That is a semantic argument. I can counter it with a semantic argument of equal or higher value. Heterosexuals are allowed marry one another; homosexuals are not allowed to marry one another. And while I might technically agree that homosexuals have the same right, they do not have the same liberty under the law, which is to say the law discriminates against them. So in the sense that you are using the word "rights", no, homosexuals do not have the same rights as you. In the sense that I am using the word "right", their right is infringed by the lack of liberty. They ought to have the liberty to exercise their right. A desire to protect a definition of a word is not, imo, even close to sufficient grounds for legally preventing homosexuals from marriage. It seems, in point of fact, rather petty.
So do heterosexuals have the right to marry someone of the same gender?
Interesting that the anti-government, pro-liberty "libertarians" support a massive, unwelcome, government intervention into the habits and customs of the people, one which creates obligations on the part of parties that aren't even signatories, and can't even name a single public interest to justify doing so. As I said, libertarians are good for patting themselves on the back for their consistent support of individual liberty, as long as they can keep quietly redefining individual liberty in support of whatever particular hobbyhorse they happen to be riding at the moment.
Further, while you might make the argument that every
person should be treated equally under the law, let me point out that associations between people are
not persons, and the law distinguishes between those associations routinely. Bowling teams are not regulated like corporations, churches are not regulated like government contractors, and parents are not regulated like military facilities.
Marriage, as a long standing custom, has a number of arguable benefits to society at large, not the least of which that it provides institutional support for a biological imperative - namely, that as mammals, we reproduce sexually. Given that there's no comparable benefit to gay relationships, the only argument available amounts to, "But mom, you let
them do it!".
The argument for heterosexual marriage rests on a biological imperative. The only argument for gay marriage is one of equality, using a truly tortured definition of "equal". The arguments for heterosexual marriage stand on their own. Absent the existence of heterosexual marriage, what are the arguments for gay marriage?
The fact that the only argument you have relies on a claim of equality indicates the situations are not equal. You can argue for heterosexual marriage all day long without having the word "equal" come up once. Take that word out of the argument for gay marriage, and the arguments fall down like a house of cards. If you don't believe that, try making a case for gay marriage without a reference to straight marriage. I doubt you could make much of a case.