Minimum wage isn't just flat for a decade, it's not being adjusted for inflation. This means minimum wage workers have been getting a pay cut over time. The debate isn't just whether we should raise minimum wage, it's whether we should be cutting it. By allowing it to remain stagnant we're making the default decision to cut.
> This means minimum wage workers have been getting a pay cut over time. This here is the strawman of the argument. Very few employed continuously for ten years continue to make minimum wage / don't move on to better jobs.
The argument is that any minimum wage earner is worse off than a minimum wage earner the year prior, and the year prior, and the year prior, etc. By holding the minimum wage fixed, we are making the default decision that a minimum wage earner tomorrow should have less effective purchasing power than a minimum wage earner today.