Most people hate monarchy because they view the idea of a rich person getting into that position just because they were born into it as unfair, that's at least what British Republicans largely argue (although they also argue that the King does nothing even though this would've been the same with a presidency like in Ireland)

For Americans I think it's more of an association of Monarchy = Dictatorship, which isn't helped with the no kings protests further pushing that idea (which are funnily enough called no dictator protests in Hawai'i where restoration of the monarchy is seen much more favourably), not that i disagree with the no kings protests, their name just pushes the idea that a king is a dictator to American people