@Geamhradh
So your son said "Mr X had his emails on the whiteboard and I saw you have emailed him about my sister"
It's unacceptable because he shouldn't be reading his emails in class tbf.
How long was his email account projected for?
I'd definitely let him know that the class saw his email account as presumably other confidential emails were briefly visualised as well, even if just the subject and sender.
How do staff get urgent messages to the teacher without disrupting every lesson, then? Things like 'Can Jessica come to Reception at 11am as her Mum will be collecting her for an appointment, please?' or
more frequently 'Can you take your register, please?'
At my last place, there was a phone in every classroom and that drove the staff crazy. They absolutely detested people coming to their classroom to speak to them (and recently, staff have also hated that because some feel it puts them at risk from Covid transmission by crossing bubbles).
Even the emergency procedures in the case of a sudden threat to the building/staff/kids or in the area (so intruders, fires, accidents, unrest, terrorist incident, etc) are notified by email because it's silent, compared to expecting a receptionist to stand up and walk around with an airhorn whilst there's a nutter with a Samurai Sword the other side of her desk.
Of course, if you'd rather your DC get dismissed into the playground whilst everybody else is hiding under desks or behind locked doors because your teacher should never have emails open in class, that is your preference - but there's probably 29 other parents who would prefer that Mr Smith knows what's going on.
The forgetting to freeze the board is annoying, but it would not have been intentional.