Apparently, the Presence of a Minimum Wage Increases Unemployment

I feel rather silly for not being aware of this commonly-held opinion among economists, but evidently there’s quite a bit of consensus.

The argument seems to be that as wages go up more people will want those jobs, so the unskilled and young will suffer in the resulting competition for those positions.

But doesn’t that just increase unemployment among the unskilled, and not among the population in general? I mean, if you have x number of jobs, and they are going to be filled by that same number of people anyway (n), then what difference does it make for total unemployment numbers who fills them?

I guess the only explanation I could see would be employers consolidating multiple positions into fewer due to gains in productivity from higher-quality workers. But that doesn’t seem to be part of the argument.

Is anyone versed in this area enough to school me real quick?