The Underground Man hates Zverkov for so many reasons, it's almost hard to know where to be begin.
For one, Zverkov is constantly talking about his sexual exploits, and as a feudal lord he exercises his right to sleep with the virgin brides before their husbands get to. The guy is pompous, arrogant, vain, and Mr. Social Butterfly. Well, at least according to the Underground Man.
Oh, right. This raises a good point: everything we know about Zverkov we know through our narrator. Either he really is a jerk or the Underground Man is just jealous of the fact that Zverkov has what he doesn't. Check this out: "I hated his handsome, but stupid face (for which I would, however, have gladly exchanged my intelligent one)." Interesting…