Welcome finoaey!
When I first read your post earlier today, I couldn't respond, because I was so aghast and angry at what the teacher said. I agree with the others that she should definitely be taken to task about this ignorance. It's simply inexcusable in the context of teaching subject matter. Ignorance is one thing, teaching it is another thing.

As far as telling them, just do. Kids are more perceptive than we think. My son always knew I was "different" and took the BP news with total aplomb. It wasn't news to him. In an ironic twist, it was he who first "diagnosed" me(!) One time, he was leafing through a magazine and there was that ad with the lady pictured one extreme to the other. He said, "That's you." I of course said, "oh no, that's not me, not really". (He must've thought, "yeah, right!") There was one picture where the lady was on the phone carrying on at 3 am. I've never done this. Not at 3 am. That was excuse enough to justify denial for me! Lol.

Just do it. It'll be ok.