My argument for gay marriage is simply that there is no compelling argument against gay marriage.
I will indulge your straw man. I'm all for animal human marriage. Animals can not own property, so when you die your property will become award of the state. Animals can not get human rights (they are animals) so you would get the advantages of marriage, but the animal will not. They can't get insurance designed for humans or receive social security. Animals can not have citizenship.
But none of that should keep you from having a marriage.
That said, one of the rights you gave up to your government was the right to be 100% individual. In this one of the rights you lost was the ability to torture animals for your personal pleasure (we call it animal cruelty laws). So married or not,
if you live in a state that has those kind of laws you gave up your rights to have sex with animals.
A large question with animal marriage is what constitutes abuse. One right we have given up as we have decided to be a society is the right to force your decisions on another without the power of law. Legally we call this consent. Without the concept of consent you can not make rape illegal (another right you gave up, raping people). So the question is "Is allowing marriage without the consent of both parties considered abuse?" If the answer to this is yes, then you can not be married in states where they have animal abuse laws.
To deepen this question, you have to ask "Are animals property?" If they are property then you can consent for them. So this is also mute. But if they are property, they can you marry a chair? I would think so. People do marry objects, so there is tradition behind this.
http://www.ranker.com/list/13-people-who-married-inanimate-objects/jude-newsome
So this takes us to a deeper question "Do objects have rights?" If objects do not have rights then you can't give them rights. As stated before, the government can not give anything or anyone rights, only take them away. By saying you destroy property, we are not giving property the right to exist, we are removing your right to destroy it.
There are a lot of very complicated questions at the heart of animal/object to person marriage. None of these arguments apply to same sex marriage which is between to people. We have established that people do have rights and people can consent to things. So this is a silly point that is only serving to derail the conversation by using logical fallacies.