Catwoman is essentially Batman's equal, except she's a woman who uses the cat as her theme, while he is a man who uses that bat as his theme. Each character lies in a moral grey area, carefully straddling the line between right and wrong, with Batman himself not being beyond using questionable methods to get the good job done and Catwoman not incapable of surprising us with a good deed when she'd set out to do something mischievous - but Batman lies more on the "right" side of that line and Catwoman lies more on the "wrong" side. Both characters wear black, both are peak level athletes and highly adept hand-to-hand combatants and both are excellent with regards to stealth. They have been love interests on numerous occasions and it's no surprise that they are attracted to each other, given that they will see the best parts of themselves in each other.