But why does that phrase involve a cat? The earliest reference is from a 16th century British play, but it involved the concept of "worry". Shakespeare used it that way too. But
The earliest known printed reference to the actual phrase occurred in The Washington Post on 4 March 1916 (page 6): CURIOSITY KILLED THE CAT
because the curiosity of a cat literally killed it when it went somewhere it shouldn't have gone, was trapped, and died.
What I don't get is that people think the proverb means that people shouldn't ask too many personal questions. Sure, that's probably a part of the meaning, but it doesn't encompass its entirety.