As a manager, how much do I need to sit and listen to an employees complaints about me?

Well, I see this situation as either one of two things. Maybe the "troublesome" employee really does have a whiny, bad attitude and doesn't like to be told anything, because yeah, there are some people who just don't like to be told what to do and that always creates a problem at a job. But then maybe it is a different situation all together. Maybe this employee really does feel like you are targeting him by expecting more out of him. Sometimes managers do that and the employee who feels targeted becomes disgruntled. I have felt that way at a job but I wasn't really the type to constantly complain about the excessive workload. I just kind of did it and went along until I got really fed up. But in your case it seems like this employee just really doesn't want to be told anything so the best thing to do would be to fire him.