>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?).
You can just pick a city and Google median/mean salary for their school district to see that this isn't true. For what it's worth, the median cash compensation salary in my own high school district is six figures.
The smirking "a retirement plan" comment you made leaves out the important bit: it's a defined-benefit plan. The point isn't that teachers shouldn't have defined-benefit pensions. The point is that those pensions are extremely valuable, and not at all a market-rate perk in the broader economy.
It's easy to win an argument with a straw man saying "teachers are overcompensated". It'll be harder for you to contend with the argument I'm actually making.