To release your frustration and powerlessness by snapping at an innocent person or creature who just happens to be handy. Usually following a bad day at work.
1. The Chief Executive bawled out the manager, and the manager bawled me out. Boy, when I got home I wanted to kick the cat.
2. 'So, Sam, you've had a lousy day at work: I'm sorry, but don't take it out on me just because you can't take it out on your boss: don't kick the cat.
To fuck. "A kick at the cat": a fuck. "Cat" from "pussy" and its furry nature, and "kick" probably because of the similarity of the thrusting action to violent kicks.
Dude, I'm so dyin' to kick the cat tonight!