The single most important idea in economics is as something gets more expensive people tend to do less of it. So increasing the cost of hiring means on average firms will do less hiring.
Also, if a minimum wage creates a surplus of labor firms lose little by treating their employees poorly. I might prefer (1) a nice boss who provides me with training and pays me $5/hour to (2) a mean boss who will give me no training and pays me the minimum wage. A firm might also prefer (1) but a minimum wage law prevents the firm and individual from agreeing to (1).
Finally, if a minimum wage creates a surplus of labor firms will hire the most qualified people they can who are willing to work at the minimum wage so low quality workers will never get jobs even if the jobs would have provided workers with the skills needed to someday get above minimum wage jobs.
There's also a line of reasoning that criticises minimum wage as a means of unaccountable wealth redistribution, the idea being that regardless of your opinion on wealth redistribution, it should at least be a transparent and accountable process.
The concept of minimum wage is one I'm rather attached to. I have dozens of arguments for why it helps people, improves the world, etc. etc. I suspect this view is shared by most of this community, although I haven't seen any discussion of it.
I don't have much understanding of the harms that minimum wages cause; and at what level of minimum wage those harms become relevant (ie. a minimum wage that would not be a living wage even working 24 hours a day is unlikely to have any of the same problems that a minimum wage sufficient to buy an aircraft carrier an hour would have)
So what are the harms that such laws cause?