It seems to me that you are the one that needs to do the work to prove your claim, if anything the percentage of male teachers overall in schools and universities seems to have declined during the years that men should have been taking over teaching according to you.
Something that seems indisputable is that the draft didn’t have any great effect on American education whereas the NEA did.
Instead of responding to that, you come back with, "Something that seems indisputable is that the draft didnt have any great effect on American education..." ; a ridiculous assertion. An analysis of the "political leanings" data would likely show that what is closer to "indisputable" is that the draft had a great effect on American education.
BTW - I don't need to prove anything to you or anyone else. I lived it. I knew men who chose that path and still occasionally meet someone who admits to having done so. I would guess that you have too, whatever your age. If not, just ask some retired male teachers in their late 50's or early 60's, especially around Democratic Party events.