Historically, the argument against raising the minimum wage was that it leads to disemployment, that is reductions in hours or jobs among low-wage workers. This view has undergone a tectonic shift since the publication of Alan Kreuger and David Card’s landmark study Myth and Measurement two decades ago.
We have more realistic models of the labour market that acknowledge the existence of market frictions and imperfect information. We also have more advanced statistical methods, better able to isolate the impacts of changes in the minimum wage from all the other things happening in the economy at the same time (e.g., recessions, migration or shifts in industrial structure that can also affect employment).
The empirical evidence from modern studies is clear: normal increases in the minimum wage have negligible to statically insignificant impacts on employment.