That sounds like a personal issue... Do you think teachers should be held accountable for making problem students advance in school?
Referring to issues as "personal" or more accurately I assume as "isolated issues", is scapegoating by another name. Teachers Unions are pros at that no doubt. Not uncommon in politics, government, corrupt public systems, etc. (in any nation, in any time in history mind you). Hell, my daughter at age 5, 20 yards away from me falls off her bike, turns around and blames me. Finger pointing is an animal behavior.
In reality, most complex systems like these two (health care and education), have few really "isolated" issues, its relative. Even if it were an actual personal issue, in the aggregate many people make the same errors, for the same reasons, all of which like ANY OTHER ERROR can be detected, evaluated, reduced or avoided, etc. largely through changes to systems (procedures, methodology, etc.)
Think about good managers/leaders, when someone under them screws up, is it best practice to put 100% of the issue on the person that made the error? Or do the leaders/managers responsible for the overall outcome...the leaders who also managed the interviews, recruiting, selection process, the training, the checking, etc., share some of that responsibility? In a corrupt system, I agree, we do tend to let them get away with scapegoating, shame on those who let that slide.
It is trivial to design a system where one persons "isolated error" can be avoiding by designing a better system. Bringing some of our ancient systems into the modern era will happen, its just that for those that recognize it today, it can be frustrating, even deadly, that it doesn't move faster.
Even your appeal to teachers shares that same issue. Teachers are not the only ones accountable for poor education outcomes. But sharing in that accountability is of course the case, denying it continues to be absurd. In my case, I shopped until I found what I consider to be an excellent teacher. Sure my child has some responsibility for the outcome, sure the teacher, but the parent does too. Yet it goes without saying that if the entire education system were far more advanced (constant reform/improvement like the rest of our economy), all else equal education outcomes can improve.
Similarly, with a dramatically improved healthcare system, the same physicians who may make stupid errors that cost people their health and/or life, may enjoy reduced errors with minor tweaks to the way they work (perhaps even working less...)