A good overview of the case against minimum wages based on economic research & reasoning is this Cato Institute summary paper, "The Negative Effects of Minimum Wage Laws":
https://object.cato.org/pubs/pas/PA701.pdf
(This understanding was popular enough in 1987 that even the NYTimes endorsed it in an unsigned, editorial-board opinion piece – that meaning "this is the consensus opinion of the paper's editors": https://www.nytimes.com/1987/01/14/opinion/the-right-minimum... )