It's a burden as a hero, you & your family had to be perfect to the public. Maybe that's the reason why he & his family didn't go for a therapy....poor touya was ignited by endeavor to surpass all might since a child but just end up felt abandoned by his own father...the way endeavor deal with the situation was really sick...he had to confronted & support touya saying that his power was self distructive but he still proud of him, not by creating another children... Well, you are creating your own enemy...
Sssiiiiiiiiigggghhhh.............................................................................................
Mental health is stigmatized enough without it being propagated in media of all kinds.
Also, yes, Touya has a tragic backstory. He grew up to be a piece of murderous garbage, and while Endeavor certainly deserves a lot of the blame, so does Touya. He got obsessed, refused to stop even though his family begging him to stop, and decided murdering people was ok. Endeavor certainly did not push him into killing, he decided that on is own.
You can still like him as villain, I'll stick to hating Dabi.
Your child is self-harming because he wants to succeed at something he hasn't yet. This has been going on for some time. Upon confronting the child he confesses to feeling pressured to perform. Should probably take him to therapy...
Everyone in this family could have used some therapy, and Endeavor being in a high risk profession should probably have a specially designated mental health service he (and family) could easily turn to for these sorts of things. I can't remember if this has ever been addressed plot wise though. But then again there is a storied and proud tradition in superhero comics of ignoring the mental health industry and/or outright vilifying it. ¯_(ツ)_/¯