Another way to look at this is that their brains are so broken chemically that they actually believe the world, including their family, is better off without them.
I just want to underscore your response to the parent.
For most of my life I've prided myself on my psychological resilience. But a while back I experienced a brief period where all the mindfulness, CBT, journaling, exercise, therapy, what-have-you were powerless to combat what was going on in my head. I got lucky and eventually it seemed to just pass. Who knows if it will rear its head again.
The whole episode increased my empathy for people like Heather.
I guess there could be multiple things going on then, one is irrationality (like what you mentioned) and the other is self-centered behavior. I am guessing it could also result from loneliness or not having good relationships with people.
Nobody disputes that they have a troubled mind and are feeling various forms of depression or pain, but that doesn’t necessitate ending their life.
Just more broadly speaking, any animal that opts to kill itself has a severe mental issue. It just doesn’t make sense from an evolutionary psychology point of view. The priority should be in seeking treatment. But I don’t expect irrational/self-centered/depressed people to all reach this conclusion.
Edit: I also personally have had a very troubled mind from time to time. I was diagnosed with bipolar in 2009, but went off meds on my own will a couple years after (not sure whether it was an accurate diagnosis). I now am happily married and expecting our first child. But I can relate a bit to these sorts of feelings.
In the end your mind is just your mind, thoughts are just in your head, and you can have a happier life once you realize this. You don’t have to identify with what goes on in your head. It’s like a radio channel that won’t turn off but you don’t have to give too much importance to negativity.