I've spent my life researching economics. If econ 101 solved all of our problems, I would be out of a job. People who think that way are dangerous. The world isn't black and white. It doesn't sound like you understand that.
Econ 101 is a misnomer of course because economic understanding developed over thousands of years starting with Plato really (however misguided he was on the topic). There is much to learn still but it sounds like you are just looking in the wrong directions.
That's needlessly provocative, and one of the more absurd uses of "no offense" I've seen in recent times...
"If you think minimum wage laws don't harm anyone you're terribly mistaken."
I don't think the parent said that (at least anywhere I can find it up this thread). One can believe that a policy hurts some of those it intends to help, and still believe that it does on balance substantially more good than harm. You seem to be engaging in precisely the sort of black and white thinking that the parent was cautioning against.
With regards to minimum wage in particular, in isolation it clearly hurts those it excludes from the workforce in the short term. However, when assistence is frequently tied to "looking for work" and not turning down job offers, then things potentially change. I'm not at all sure that a general minimum wage is a better solution then saying "jobs below $X don't count toward assistance", but I'm not at all sure of the opposite, either.
The argument against the minimum wage is in the realm of deductive reason and not something you look around for proof of or proof against. It's basically the economics equivalent of 1+2=3. If there are problems with that equation we need to analyze it in its' space and not look around for cases when we think 1+2 != 3. The problem with verifying laws of economics is that we don't know what we're seeing the effects of in reality. Cultural, weather, moods, government policies, etc. could impact what we're seeing in data without it being clear why or how. Empiricism can inform our analysis or can give us new routes to inquiry on but it can't be used to argue for or against the laws of economics as we understand them. I'd avoid reading economic studies of anything for this very reason.
Regarding the second half of your comment, it's certainly true that there can be confounding variables, but I think avoiding empiricism does far more harm to reasoning than relying upon it. There is an infinity of internally consistent models. Most of these will have nothing to do with reality. In order to tell which actually represent the world we're living in, we need to look at the world. Intuition alone has proven a poor guide in most other sciences.
I think this is not based on evidence. Not all minimun wage laws are bad. For example:
https://en.wikipedia.org/wiki/National_Minimum_Wage_Act_1998...
I'm sure the minimum wage could be set to a level where it would do damage, but I don't believe that is necessarily so.