Consider:
-holders of advanced degrees and credentials (gatekeeping)
-assigns labour (literally called worksheets!) to pupils (proles)
-gives out sanctions, extra work, and bad reviews to punish bad work behaviour
-literally trained in discipline
-sharing of knowledge is forbidden, calls it cheating
-insists that you not work directly with your best friend, assigns you pairwork with a gender you're not yet comfortable with
-according to most media, teachers are the most liberal profession
-creates quarterly performance reports for workers, stressing constant need to improvement (report cards)
-have direct access to whiteboard markers and notebooks, the means of instruction!
To add on to that, they even have significant amounts of capital! They get paid tons, relative to the proles allowances. They also use a lot of their money to buy school supplies, and the school supplies are used to do their job, which produces money. Teachers literally do M-C-M.