There are multiple reasons why humans and animals have different languages. First, when animals are separated for extended period of time, languages begin to differ from each other. Language is constantly changing, very slowly, but changing. Look at human language. It varies a lot in different regions of the world. Even birds, like the brown-headed cowbird in California, have slightly different accents and song preferences based on where they are from within California.

Second, animals live in different environments where some methods of communication work better than others. For example, animals that live in dark caves may use a visual language or tactile (touch). In other environments like thick forests, sound is the best method of communication because it can travel the farthest.

So each animal group has evolved its own language based on isolation from other animals and by taking advantage of the best method of communication based on its own environment.