Hurting is preferable to dead any day of the week ya know? You don't recover from dead.
I agree with you that suicide shouldn't be the answer when someone has kids, but I don't think the quoted part is necessarily true.
There are many people who live in genuine misery and agony due to combinations of mental issues and physical pain. They know it will never go away, and it will never get better. Take someone with both schizophrenia and depression for example, it is a lifelong and mostly incurable combination of diseases. People assume it's possible to get over depression, but only because they haven't had legitimate clinical depression which is very different from just feeling sad. It does not go away, ever, with or without pills. Every day the person hates themselves, has no joy in life, no desire to do anything, and no energy to the point where some people legitimately cannot summon the physical energy to go outside at all for weeks at a time. Combine that with something like schizophrenia where they hear voices and can't tell reality from fantasy for their whole lives... and I can see why they would not have any desire to continue living.
They already know it will never go away and they will never feel better, so their choices are go through decades of continued misery and self-hatred, then die eventually anyway, or just speed up the process of death but skip the decades of misery part. To many people it looks like a very appealing option. I honestly can't fault them for thinking that way.
Pets are put down all the time as a form of mercy and to save them from pain, even though they cannot communicate whether they want to die or not, so why should it be any different for a person who actually is able to communicate that they want it to happen? It is their life, and regardless of anything else they should be able to control what they do with their own life, including ending it to save themselves a lifetime of suffering if they believe that is the best option. It is certainly selfish to do it when they have children and family members who depend on them, but ultimately it is still their life and they are the ones dealing with the pain every second of every day, not the people around them.