Because they do. But when the movie came out, people loved it. It broke every box office record, and people stopped going on about cat faces and Smurfs. Why?
Because while the Na'vi were clearly cat-based, no one said as much in the movie. It wasn't like the story of Pandora was that once upon a time a zoo ship crash-landed and the crew was forced to repopulate the empty planet with the help of the pumas in the cargo hold.
Now compare that to the Thundercats. Every character is named after a type of cat (Lion-o, Panthro, Tygra, Cheetara). The characters in Avatar just pretended like they didn't even know cats existed, and with all the other stuff going on, it was easy for the audience to forget too, beyond noticing that the characters were graceful, quick, athletic and beautiful. You got the aesthetic of a cat-like creature without calling the movie Avatar: Planet of the Noble Cat Warriors.
Hell, maybe James Cameron just accidentally made them look like cats, like George Lucas keeps accidentally making aliens talk like stereotypes of various Earth ethnic groups. Maybe he was just trying to make an improved version of humans, and accidentally wound up in the same place.
Either way, why don't we just declare Avatar to be the pinnacle of human/cat hybridization and let it stop there? After all, look at this guy:
That is an adorable, stupid kitten without a brain in its head, and it's perfect the way it is. Let's end this weird-ass compulsion to merge them with us, before genetic scientists start getting weird ideas. You don't want your grandchildren to walk down the streets 100 years from now and see this:
For more modern ideas that were here before us, check out 4 Reasons 3-D Movies Don't Have to Suck and 5 Multiplayer Video Games That Will Destroy Your Marriage.