Except when we do, but it doesn't make for flashy press releases. Pet owners, vets, farmers throughout history - anyone who lives alongside animals, cares for them, and is open to developing an emotional relationship with them, knows animals are more than just small finite state machines made of meat. But it takes time to spot and learn the patterns of behavior, and as I said, it's a two-way street; the animal has to "open up" and learn you as much as you have to learn them.
It is a kind of thing that's difficult to cleanly verify and reproduce, and it's also kinda mundane. The cases that made headlines look like Clever Hans the other commenter mentioned.
I imagine that a better classifier, some general AI system that gets to learn and observe the animals, would be able to tease out the patterns and then translate them to English, and then that would be reproducable and make for flashy headlines.
The real lesson we should have learned is that horses are stupid and we should have been testing a Border Collie.