An argument that opponents of gay marriage make is that legalizing gay marriage will inevitably lead to legalizing polygamy, which would be a bad thing, therefore gay marriage shouldn't be legalized.
As a syllogism, it's not invalid. If the premises are true, the conclusion is too. If gay marriage actually did lead inevitably to polygamy and polygamy actually were a bad thing then gay marriage is a bad thing. But neither premise is true, so the conclusion doesn't follow.
I don't think there's anything inherently wrong with polygamy. Past implementations of it have been sexist and bad, but then again, past implementations of regular marriage have also been sexist and bad.
And gay marriage won't lead inevitably to polygamy because they're two separate issues - and polygamy is significantly more complicated. To change straight-only marriage to include gay marriage, all you have to do is replace every instance of the word "man" and "woman" with "person" and replace every instance "husband" and "wife" with "spouse". It's not like the husband gets certain privileges the wife doesn't, at least, not anymore.
But to generalize marriage to more than two people takes more work then simply replacing "two" with "two or more", because a lot of the ways marriage currently works assumes that there are only two people involved. For example, when one spouse has a medical problem and is incapable of making a decision about what to do, the other gets to decide. How would that work if there's more than one other? What if they disagree? Also, is marriage a transitive property? That is, if A is married to B and B is married to C, does that mean that A is married to C? These are questions that never arise when marriage is restricted to pairs.
I don't have any answers to those questions, but they'll need to be answered to legalize polygamy. And legalizing gay marriage doesn't get us any closer to answering them, which is why it won't inevitably lead to polygamy.