I used to make jokes about how if humans aren't animals, or plants, then they must be fungus.
...Well, other animals have been known to engage, or at least attempt to engage, in bestiality or humanality. Like, emus and orangutans have been known to be sexually attracted to humans, a lot of dolphins will fuck anything willing (and some male dolphins don't even care about the "willing" part), rabbits have been known to have a thing for cats, wild hogs have been known to go after anything roughly their size, and so on. But in general, creatures stick to their own species, humans included.
The biggest argument against marrying a dog or a pig is there's no evidence they can understand the implications of a marriage contract. That's also sometimes true of a severely mentally disabled human, but most of us wouldn't call them mere animals in a way that implies other people aren't.
Also, humans meet the definition of being mammals. It would be very strange if there was a mammal which isn't an animal. A better way of saying it is that humans are people, but non-human animals are not presently recognized as such.