But it is about economics. The theory of the minimum wage is that you take money from some hypothetical fat cat capitalist who would otherwise have stored it in a mattress to no avail and instead give it to a hard working stiff who can benefit their lives with it.
The problem is that there are also a multitude of other things that can happen instead, pretty much all of which are bad and do actually happen in practice. The money may come from someone other than a fat cat, like a local small business owner or a working class customer. If prices rise, local businesses may be less competitive, resulting in higher unemployment and a smaller tax base (resulting in lower tax revenues or higher tax rates or both). The working stiff may lose their job. In the worst case, the entire business may close down. It's quite a bit worse than cutting in line.
If you really want to understand the problem, list every consequence can think of for a minimum wage of $1000/hour. Most of the problems still apply at $15, just at a smaller scale.