Why are humans the only animals that can speak?
Humans are not the only animals that can speak.
Humans are the only animals that can speak words, as we define words.
Almost every animal speaks. Go out of your house in the morning and listen to the birds talking. Each bird knows what another is saying, and there are a hundred conversations going on at once. Birds constantly talk; they're gossips.
If you live in a city, you can hear the squirrels talking to one another as well, if you pay attention. They're usually only talking about food and sex, but that's really no different from the average male college student.
Even our favorite animals, cats and dogs, are constantly talking. Dogs are probably extremely frustrated that we don't understand their woofs and whimpers, because dogs DEFINITELY have a lot to tell us. They can understand us, to a certain extent, but it's not quite the same without a two way connection.
Cats usually don't talk as much as dogs, but they do have a more complex language than dogs. They have different meows, growls, hisses, purrs, etc. I've spent enough time around cats where I know what they're trying to say for the most part, but I often find myself wishing that I knew exactly what they were saying. It would be so much easier. I love my kitties.
So yeah. Humans aren't the world's exclusive talkers. We just don't understand any spoken language but our own. Maybe that'll change with time. Who knows?