I think you'd be right if this manga was about teaching, or for teachers.We as readers know exactly what Miina has been experiencing and her motivations etc. But Takayanagi does not have that extra information. He only got what he's seen and what Miina has told him.
Leaving a quote and walking away based on that limited information is quite negligent as a teacher. At the least he could have pointed her towards a school counsellor or something. Ignoring kids who've self harmed is how you can end up with dead kids in the real world.
In my opinion this manga is about philosophy and it's class, so it'd make sense if it only talked about using philosophy for answering teenager's problems and never about actual protocols used by real teachers.
But that's only if I'm correct. The title gives a hint, idk.