If committing suicide seems selfish to other people, isn't talking someone out of killing themselves an act of selfishness also when he/she has a valid reason to want to die?

It's not like you can make their problems disappear when you talk them out of suicide. Seems to me like their suffering is just prolonged and you're acting on the premise that you don't want to lose them. You just don't want to suffer losing that person who wants to die.