We don't admit it often, but the way our society "behaves" is still largely based on religion. Sure, you might be an atheist, but you act like your parents, neighbours and friends acted, and they acted like their parents acted and so forth all the way into the dark ages (wasn't it really weird when you went to China once, and there people eat insects on sticks as sweet treats? Bah, who would eat an insect? The answer is: People who are used to that as they were brought up like that).
And the Christian religion, assuming you are in America or Europe, states in Leviticus that you shall not have sex with an animal. The punishment is death. It's right next to the "kill the gays" phrase in the bible. On the other hand, the bible also says we can dominate the Earth, multiply and rule the animals as we see fit. So there is the anything-goes card for killing and eating them, if we decided they are delicious when cooked. Religion is mostly cherry-picking, so over the aeons people cherry-picked and agreed to eat animals, but to feel holier and better than some people to be condemned in mass next Sunday for animal buggery.
That should answer your question. However, interesting observations:
From then on, it is simply a quick opinion people form when prompted on this question nowadays. Most find it revolting, or extremely unusual. However, since we all learned just recently that we can't e.g. tell the gays they are to be put in jail for being disgusting (our parent's generation did that, amazing, right?) - people make up justifications of their opinion/gut-feeling after the fact to dress it up with logic for a better argument. I have no problem with someone saying it's disgusting in his mind. I find fresh born babies utmost disgusting, or the taste of rhubarb e.g. The problem is when people start to pretend their point of view is the "logical one". The first and easiest thing is consent. Oh, the animals can't consent. Whoever says that - you immediately know he is just making it up based on some instantaneous idea he just formed in a heartbeat. For example, I am pretty sure if a male dog mounts a female human and starts, well, doing her, we must assume consent on the side of the dog. Otherwise he'd stop and dismount once he realizes his error. Yet he doesn't. Also notice that the argument typically states "the animal can't". This is categorizing - e.g. highly intelligent - dolphins together with pigs, goats, horses, dogs, deer, cows etc. Do ALL these animals - on a fleeting inspection - look similar enough to you such that a broad generalization can be made for all of them together within "the animal", that "can't consent"? I don't think so.
Then they move on to other things. The most hilarious straw typically grabbed is "public health". As if one person having sex with a dog is a better entry point for diseases into humanity than the millions of "normal" dog owners who normally sleep with their pets in their beds, or have their faces licked etc.