"Care will kill a cat."
A year later, in 1599, Shakespeare, in Much Ado About Nothing writes,
"What, courage man! what though care killed a cat, thou hast mettle enough in thee to kill care."
"Care" at the time meant worry or sorrow, and was not at all meant to reference the inquisitive.
At some point, we "evolved" and the saying become "curiosity killed the cat", meaning that being too inquisitive would lead you to trouble.
The explanation is that this "evolution" came about during the Industrial revolution when we needed to create factory workers, people who would do as they are told and not seek out answers, ask questions, or otherwise be curious.
Interesting how we as a people are actually scared of the creative, curious nature.
Sounds like it's time for a Creative Revolution!