The counter-argument is that many workers do not have a choice; they will always accept wages vs nothing, but have no power or ability to negotiate.
With a minimum wage we've made the decision as a society that, in order to prevent worker exploitation, we will also eliminate certain classes of work. Some of this work does vanish entirely, while some of it reappears in the shadow economy through untracked cash payments or self-employment.
As with all policy decisions there's a messy balance here and we're arguing mostly over where the line falls. I do wish there was a cleaner way to protect against monopsony (higher minimum wages) while also providing good opportunities for low-skill workers (those who are very young, very old, have physical or mental impairments, etc).