Cats most certainly CAN be taught. They're animals, and ALL animals, right down to amoebas, respond to classical conditioning. That's all you're doing with a dog (or a child.... oh wait, did I say that with my outside voice?) when you train it. You associate certain behaviors with reward, and those behaviors increase in frequency. That's called positive reinforcement, and it's the most effective training technique.
Picking up a cat and throwing it around when it does something unattractive is negative reinforcement, and while it works, it tends to foster less than sympathetic feelings for the trainer on the part of the trainee. Think about how cadets feel about their Drill Sargeant; boot camp is a classic example of negative reinforcement. And your little recruits have very sharp claws and teeth, and have access to you while you sleep. Think about THAT when you're showing the cat who's boss.
I know a woman who has clicker-trained her cat, just like she did with her dogs. It took longer, because a dog has more desire to please built in as an instinct. It took a lot of patience and consistancy, but it worked.