Slash's reasons for leaving are twofold. One, he is in love with Stephanie. Two, every once in a while a great guitarist has to take a break to bust out an awesome guitar solo. It’s just an urge they have, not unlike a smoker’s urge to smoke or a non-smoker’s urge to pee.
Here are some other documented incidents of Slash taking an awesome solo break.
After he’s done with a solo he just tosses the guitar aside like a cigarette butt.