John Cochrane may have written the most concise argument that economic theory should be rejected:
Economic theory also forces logical consistency that would not otherwise be obvious. You can't argue that the labor demand curve is vertical today, for the minimum wage, and horizontal tomorrow, for immigrants. There is one labor demand curve, and it is what it is.
The conclusion should be: Therefore, we must reject the concept of a fixed labor demand curve.
Overall, Cochrane seems to get the concept of science wrong. A few days ago, I noted that Cochrane does not seem to understand what economic theory is for. Now he seems to misunderstand what empirical data is for.
See, the issue is that no one is "arguing" that the labor demand curve is vertical for the minimum wage. No novel theory is being constructed to give us a vertical labor demand curve. The studies are empirical studies. The empirical studies show if there is such a thing as a labor demand curve, it must be vertical for the minimum wage. But really, all the studies show is that raising the minimum wage does not appear to have a disemployment effect. The "Econ 101" approach pictures this as a vertical labor demand curve. And that would be fine on its own.
Likewise, no one is "arguing" that the labor demand curve is horizontal for an influx of workers. Again, no novel theory is being constructed to give us a horizontal labor demand curve. The empirical studies are only showing that an influx of workers does not lower wages. The "Econ 101" approach pictures this as a horizontal labor demand curve. And that would be fine on its own.
But those two results do not exist in a vacuum. If you try to understand both empirical results with a fixed labor demand curve, then your only choice is to reject the fixed curve. You have two experiments. One shows the labor demand curve is horizontal, the other vertical. Something has to give.
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Now there is a way to make sense of these results using information equilibrium. Here are several posts on the minimum wage (here, here, and here). The different effects of immigration versus other supply shocks are described in this post. If you are curious, click the links. But the main point is that when we make "Econ 101" arguments, we are making lots of assumptions and therefore restricting the scope of our theory.
In order to obtain the Econ 101 result for the minimum wage and immigration, you essentially have to make the same specific assumptions (assume the same scope): 1) demand changes slowly with time and 2) supply increases rapidly compared to demand changes. The commensurate scope is the reason why the Econ 101 diagrams are logically consistent. But they're both inconsistent with the empirical data. Therefore we should question the scope. Under different scope conditions (i.e demand and supply change), information equilibrium tells us increasing the minimum wage or increasing immigration increases output ‒ meaning that you should probably accept that demand is changing in both cases. Which is the point of higher minimum wage and pro-immigration arguments: they create economic growth.
As an aside, I think the a lot of the right-leaning economics might stem from assuming demand changes slowly. The cases I just mentioned made me think of a case where Dierdre McCloskey seems to be assuming demand changes slowly to argue against Thomas Piketty.
In the same sense that while you can obtain an isothermal expansion curve  from a restricted scope of an ideal gas (that scope being that temperature is constant, hence isothermal), if your data is inconsistent with the theory you should begin to question the scope (was it really isothermal?). Unfortunately, Econ 101 ‒ and for that matter much of economic theory ‒ does not examine its scope. As Cochrane says: it's about "logic". Logic has no scope. Things are either logical or illogical. That's not now science works. Some descriptions are approximate under particular assumptions (constant temperature, speeds slower than the speed of light) and fail when those assumptions aren't met.
Given empirical data requiring contradictory interpretations of theory (different labor demand curves), a scientific approach would immediately question the scope of the theory being applied. What assumptions did I make to come up with a fixed demand curve? I definitely shouldn't assume studies that contradict the theory are wrong.
 Actually, in information equilibrium the Econ 101 demand curve is essentially an isodemand curve (i.e. a curve where demand is held constant/changes slowly) analogous to an isothermal process using the thermodynamic analogies. If I say the minimum wage won't decrease employment because it increases overall demand, the Econ 101 rebuttal is to come back and say "assuming demand doesn't change ...". It'd be kind of funny if it wasn't so perversely in the defense of the powerful.