Well, the answer is simple to me : the well-being and happiness of other persons, especially my relatives and my friends, but also other humans in general are part of my terminal values. So I care about what will happen to them after I die, as long as they'll be alive. But I don't care much about what would happen after all humanity is wiped out, if that were to happen.
More than once, I've had a conversation roughly similar to the following:
Me: "I want to live forever, of course; but even if I don't, I'd still like for some sort of sapience to keep on living."
Someone else: "Yeah, so? You'll be dead, so how/why should you care?"
I've tried describing how it's the me-of-the-present who's caring about which sort of future comes to pass, but I haven't been able to do so in a way that doesn't fall flat. Might you have any thoughts on how to better frame this idea?