She's their boss.
Not really. She's the head of the union. She pretty much has to do what the rank and file say. Her power, such as it is, comes from the control of tens of billions of dollars in the pension etc.
That might be true in theory. In practice, the bosses run the union.
Besides, my point is that the teachers' unions are run by people who think math is big and scary.
Silly bunny! That's not how it works. If it were, then why would 90%+ of union contributions go to RATs when the membership is nowhere near 90% RAT?
Where did you get the idea that a union was democracy in action? Have you ever tried to go against a BA or Sec/Treas of a local?