It's basic human decency to stop the car if you have hit a cat. Even if you don't love cats, the chances are good, there's another person who loves the one you have just hit and will be devastated, not only that they were injured or killed, but that nothing was done to help.
It is also crucial to remember, that statistically, only 25% of road traffic accidents involving cats are fatal, so the chances are good the cat can survive with urgent care - instead of being left to suffer a needlessly slow and painful death because they were abandoned at the scene.
If you have hit a cat while driving, the chances are good that you are in a residential area and not a busy motorway. In this situation, stopping the car will in no way put you or other drivers at risk, so should not be a reason to keep driving and leave the animal.
As much as you may not want to confront what has just happened - the owner of the cat is counting on you to do the right thing and the decision you make in this crucial moment can be the difference between life and death.