Why is a catsuit called a catsuit?

After having looked for possible answers myself, and found that covering bodystockings tened to be the go-to outfits for catburglars (mainly female ones) in cinema, that do seem to be the origin for the "cat" in "catsuit". Do note that "catburglar" originally seem to have to referred to thieves that snuck in more stealthily to steal valuables as opposed to regular burglars that could just as easily use violent means, the "cat" thing then referring to the stealth.