Teachers don't count as slaves you can give up to Cass, but do count towards the 3 you need for the first scene after giving up Sarah or helping Cass enslave her (depending on if doing the Rosa route or the Dan route). Only other students, and the non-Adult NPCs, count as ones you can give up to Cass.
Also if you get Cass to Level 20 before having gotten 3 slaves of your own after having given up Sarah, you'll get a trio of extra scenes where Cass laments how boring it is only having you and Sarah as slaves, and if playing as Dan, leads to a way to swap to being Rosa.