You should try thinking about this in a different way.
What your describing does fit the pathology. You only seem to be approaching the issue from one angle, always the same one, so you can only ever reach one conclusion. This is textbook depressive pathology right there.
"it all ends, so why care at all", this is a false approach really, because what is happening until it's over? The journey is more important than the end, cheesy as this sounds. If you were to genuinely only care about the final outcome, you'd go skip right to that point, if you catch what I am saying. As you have written this and and as you are struggling with the question still, this clearly is not the case.
Sit down and think, are you truly being honest with yourself, is this genuinely what you believe?