Oh, look at that, you don't know what you're talking about.
Let me put on my surprised face.
I literally started this discussion asking for context on situation since i lacked it.
Then i went on arguing hypothetical apocalypse specifically because no one managed to give me a bloody context.
Even if you did have a clue, all you're doing is adding the question of "length" to the weight of a human life. A little girl's life has no inherent value because she's going to die soon? How soon does it need to be? A year? Ten years? Are terminal cancer patients disposable, or people with brain conditions that might kill them in twenty years or ten minutes or never? Are people who live unhealthily and so are shaving decades off their lives less human and valuable than people who keep themselves trim and maintain a healthy vegan diet?
If we assume I live to be 100 years old (by no means a guarantee), I've got only 75 years left in me. So is sacrificing me a totally different prospect depending on whether the apocalypse is seventy or eighty years from now?
Your stance is incoherent, because you're approaching this emotively instead of building on a clear axiom.
Human's value is entirely dependent on others. On its own it has no inherent value, since universe is a cold bitch, but it has value to people around you. To certain person, some lives are simply way more valuable than others. You give way more fucks about your friends and family than you do for some random guy dying in Africa.
"Length of life" is irrelevant concept here, and i honestly don't understand why you cling to it so much. You want to stop death of people you care about because you don't want them to die - they mean more to you regardless of "length". You are trying to assign some sort of objective value to every human, failing to realize that its worth is subjective to each human and ever changing.
In hypothetical scenario where world would end tomorrow if Miyu is not sacrificed, both parties would be correct in their actions. What's-his-name cares more about himself, his family/friends and the world than he does for Miyu and he is right for trying to sacrifice her to save all that, while Shirou cares only for his sister, as she is more valuable to him that everyone else combined(value of human life is not stackable, which is why "a million is statistic" exists. You probably care more for your parents than you do for continent-worth of unknown people) so he is correct to give them middle finger and ship her off world.
From their personal perspectives, anyway.
As for actual scenario, i still don't know enough to make educated comment, but it does seem rather improbable that he can't come up with another solution that would resolve this situation without sacrifice in a thousand years. Not to mention that value of world in that timeframe should be lesser than one of his friend's(?) sister.
