@Cassandra it's irrational when depression tells you there's nothing worth living for.
We will have to agree to disagree on this. That might be true; it might not, depending on the individual circumstances.
It's different if you've really thought about your life soberly, with an objective evaluation of your presence and probable future.
Here we can agree.
I think it is possible to look at your life soberly and objectively, find the prospect of your present and probable future objectively depressing, without rational hope of being better, and make a completely sane, if sad, decision to off yourself.
Most of us do not come to that conclusion. Some, unfortunately, come to that conclusion when things would or might well have improved, and that is tragic. (I think this poor boy was almost certainly among them.) But I do not think that therefore everyone who is depressed is necessarily irrational, nor do I think suicide is necessarily irrational or a sign of mental illness.
Shiny, happy optimism and a zest for life are not necessarily rational (or irrational), either.
ETA:
But really, that's all a derail. I don't think this particular boy made a decision based on a sober and objective view of his prospects. I think he was a sad and confused boy who was looking hard for reasons to go on, and he was pushed over the brink by a heartless sociopath with whom he tragically fell in love.
The fact that he kept pulling back is heartbreaking -- I am firmly convinced that if it weren't for this horrible, evil girl, he'd be alive today and would likely have gotten the help he needed.