People don't like to think that anyone's labor is worth less than the minimum wage. Someone might end up flipping burgers for $5.00 an hour. You might think the minimum wage is a way of paying some sort of dignity premium -- hence language like "living wage." People with such good intentions look at the direct beneficiaries of these policies, say, burger flippers now making $7.50 an hour. They pat themselves on the back. But they rarely count the invisible costs: willing human beings who never get hired in the first place.
But $5.00 an hour is not enough to live on!, they'll say. For whom? A teenager living at home with his parents? An elderly person who wants simply to stay active? A single mom with three kids? A single woman sharing an apartment with 2 roommates? Of course, not all of these people could live off of $5 an hour. But some of them could given the opportunity. Concerns about those who couldn't don't justify minimum wages even if we ignored the invisible costs of the policy, which include reduced margins to businesses that might otherwise grow (and hire more people).
In other words, if you pull take off the bottom two rungs of the income ladder, many will never climb it. That's the effect of the minimum wage.