I know this thread was a year ago, but the actual definition of brainwashing is removing a person’s ability to think for themselves and they instead begin to think as they have been taught, without any intelligent thought processes behind it. Brainwashing tends to involve a lot of parroting, and the brainwashed person will simply repeat themselves (sometimes word for word) without actually being capable of explaining what they are parroting.
Missionaries are a good example – they have absolutely no idea what they are talking about and just keep at the same nonsense they have been taught.
I personally have not experienced any brainwashing in chinuch – yes, there are ideas that have widespread influence, but on the whole, girls who go through the BY system can think intelligently for themselves (most of them, anyway).