Cats don't wag their tails because they use their tails to help balance them. If they wagged them, that would disrupt their balance and make walking more difficult.
Unlike dogs, cats do not wag their tales when they are happy, instead they will purr. However if a cat is angry, annoyed or hunting they will wag their tails; sometimes just slightly other times vigorously.
Because they don't have sensitive sense of smell like dogs'. You might not believe this but dogs wag their tails because they don't want to smell their stinky butts. I saw that on Animal Planet.
