Minimum wages are an artificial price floor for labor, designed to counterract a structural deficiency in the quality and necessity of work. It's a belief that, if we let the market do its own thinking, an unacceptable number of people would be incapable of providing services worthy of a living wage. For instance, a kid grows up on the wrong side of town, crappy school, can't get out of the cycle, so even if he is motivated, he can't earn a position better than burger chef manager, and winds up spending most of his life just getting there while everyone else gets ahead. That's a valid concern.

The argument against minimum wages stems from the economics of inefficiency. It's supply and demand, basically -- when you move the minimum wage up, you create a situation where more people want the job and less businesses are willing to hire out at that rate. Generally speaking (and people fight about this all the time, but generally speaking) a historical analysis is consistent with that; some would say, history bears this idea out completely, meaning, it's demonstrated in the real world and not just on paper. Besides that argument, there's an element of 'My business is my business' to it, as in, it's not your job to tell me how much to pay my employees. Those are each valid concerns as well.

Personally, I don't have a problem with *a* minimum wage. It's not an economic thing (the people who argue that min. wages are good for the economy are wrong, I think, but that doesn't mean that minimum wages are necessarily bad). It's a social thing, and we're allowed to make economic policies for social reasons. If we all understood the economic impacts of those policies, we'd have much better luck in making them work. There are practical reasons why you can't just arbitrarily set the minimum wage at, idunno, ten thousand dollars an hour or whatever -- most people aren't asking for that.