It's bad enough that we have to contemplate our own mortality and that of those we love and care for, but our understanding of our state of affairs is forcing us to contemplate the reality that species don't last either.
Humans, being a species, are not immune, so it's certain that at some point down the line there will no longer be anything recognizably homo sapiens sapiens.
The first thought we tend to have about this eventuality is that it's a disaster, and I'll agree that if were talking about (geologically) sudden extirpation of our kind, say by asteroid, it's pretty easy to put it on the VERY-BAD-NOT-GOOD side of the ledger. But say that in, oh, maybe 400,000 years the earth no longer hosts a single human being, would that be a bad thing? What should we feel about such an eventuality?
It could depend on how the disappearance came about. Would my australopithecene great-to-the-Nth grandfather lament the differences between Lucy and my daughter Claire? Should we see ourselves as their triumph through the ages or the record of their eventual downfall? If we view it as triumph, than if we are simply displaced by a new branch of evolutionary descendants, we should see it as surviving. After all, we already know our descendants are going to be a little different, if they eventually become a lot different, how bad would that be?
On the other hand suppose our ecological niche slowly disappeared and our numbers dwindled down to zero. Or a virus evolved that impaired our ability to reproduce with the same result. Would that be so awful? If so, why?