If the claim is "nurses and teachers are poorly paid in the US", that claim is broadly false. K-12 teachers in major metro areas in the US have surprisingly generous comp packages: well above area median take-home salary with predictable ladders, very good benefits, and defined-benefit pension plans.
There are school districts where teachers are poorly compensated, but they aren't the norm over the population as a whole. Teachers are generally well-compensated.
Nursing, I don't know where to start.
>that claim is broadly false.
No, sorry, no, it is not "broadly false." K-12 salaries enter at average 40k often with a requirement to enter a graduate program within five years. I don't see that teachers in most states have received substantial increases in salary over any considerable period. They are underpaid.
Compensation rates are not "surprisingly good" (surprisingly?). Both groups merit much higher compensation. Your subjective consideration of "well-compensated" may differ from mine and fair enough, but I find generally one's position is more an index of their political beliefs (or sentiments towards unions in general) than any objective standard of what is "surprising" ("a retirement plan? In this economy?).
> well above area median take-home salary
For someone with masters-level education and years of experience?
Folks may talk past each other on this.
Some people may say that nurses and teachers ARE NOT well-paid because those workers deserve to be paid more than they are.
Some people may say that nurses and teachers ARE well-paid because they are generally paid more than median wage.
As for some dry facts, median wages:
https://www.bls.gov/ooh/occupation-finder.htm