Their entire argument seems to be based on "the pay gap calculation is dumb", but the problem is, even if that is true, that doesn't disprove that teachers are underpaid.
The point about teachers having above average pensions is a good point.
Salary correlating with required skill level also misses some of the point, I believe, because qualitatively speaking, skill level isn't the most driving factor behind choosing to become a teacher.
The "if teachers aren't paid well, why aren't we seeing more of them quit?" is a lousy point. Some jobs are simply more important than others, and its jobs practitioners know that. They are less likely to quit.
I wonder if there's a way to calculate replacement cost. Like, what the long term damage to society would be if 20% of a particular work force disappeared. That might be a better way to estimate how much teachers should actually be paid.