> There are European countries with minimum and average wages much higher than ours, and they don't have those problems.
I'm sorry but I'm not sure how you would know that. You would need to compare their output currently to their output in an alternative history / parallel universe where the min wage were lower. Barring that, it's interesting that you say this but don't address why almost every EU country has a lower GDP per capita that the U.S. Granted, GDP is a flawed measurement, but feel free to look at other similar measures. The EU also has a higher unemployment rate. About double in fact.
So if I am saying that a higher min wage reduces output and causes unemployment, and you're telling me I am wrong based on what actually happens in the real world, I would have expected some addressing of these numbers. While I am not using them as proof of anything, it does seem to run counter to your claim that the "theoretical arguments" don't have predictive power in the real world.