The only arguments for minimum wage that I've ever seen, are those that claim that under certain conditions minimum wage may not be noticeably detrimental. What you never see is the minimum wage actually make a lick of difference to any metric that matters (like unemployment rate, or poverty rates, or income rates, or whatever else). Never. And I'm serious about this. Have you ever seen a region that adopted minimum wage, then come back a year later and show, for example, that poverty rates have fallen as result? Curious.

So you have a policy that cannot demonstrate it actually makes anything better, sometimes can be demonstrated to not measurably negatively affect anything, and frequently actually hurts.

Policies like minimum wage, or rent control, are not really about facts. They are driven purely by emotion and ideology.