I think what the parent is getting at is that by instituting a price floor, you prevent people from providing services whose utility is below the price floor. In other words, if someone wanted to do extra work that wasn't worth much money (but might add up over a longer period of time), they are now unable to do said work because no one will be willing to pay them for it.

Basically, when setting a minimum wage, you end up picking between two groups of labor: those who work for some extra money (think high schoolers and retirees who would like some extra spending money and don't mind doing menial tasks that may not generate much value to earn in) and those who work to live (think unskilled laborers who do laborious work and feel they are insufficiently compensated for it). A lower wage favors the former group because they are able to offer the services for less (and the quantity of labor demanded will increase if the price goes down) while a higher wage favors the latter because they can demand more money.