There's a big and important difference between caring about something and feeling/being responsible for something.

I care about an aircraft being flown safely. But for the love of God, don't put me in the cockpit and make me responsible for flying the plane safely.

Ditto for mental health of undergrads when I'm lecturing. I'm there to teach them how to implement a red-black tree. Do I care about their mental health? Of course. Do I feel any responsibility for it? Hell no.

Sometimes caring about something means NOT taking responsibility for that thing.