Private is the thoughts in your head, everything else is public. This teacher didn't need to actually say the thought out loud, it could just stay a shitty thought in their head. Maybe they could try some introspection, about why they are so frustrated over something so trivial. Maybe consider why they are so quick to have violent thoughts about people they are in charge of.
Also, besides all of this, who ever thought Snapchat was a private place, even using your definition of the word? They sent a death threat to a public company that is very clear that they monitor the content that flows through their servers.
Context matters, you can't just leave out the details and say "any privacy violation is bad". That's not how society works or else wed all be living alone in caves.