People use this expression to suggest there are several ways to do something or get something done.
Example:
It’s been quite the challenge to get support for something at work. The colleague I confided in replied that there is more than one way to skin a cat – let’s brainstorm some ideas. While taken aback at the horrendous use of this expression, their heart was in the right place to help me come up with other ways to achieve my goal.
I cannot confirm whether the following is true, but one comforting explanation for this phrase is that it’s not actually referencing skinning our cute little feline friends, but rather a phrase that originated in the American south region that pertains to the preparation of a catfish.
The question then becomes, “Who shortened it to cat?! WHO?!”