On whose speech?

It seems more and more that the elephant in the room here is that schools are part of government, but they overwhelmingly lean the opposite side of the administration and they want to exercise their speech through their positions, but the government doesn't want to allow that.

Private individuals would of course enjoy first amendment protections on speech, but if you are government you don't get your speech restricted by government, that's just government. You can't eat your cake and have it too.