Year 0: In the past, as a child, Shirou Emiya survived a magical catastrophe which killed thousands, where he is the sole survivor. This causes him to swear to devote his life to saving EVERYONE, without care to what happens to himself.
Year 100: In the future, the “spirit of the planet” offers Shirou (now called Archer) a deal to act as it’s “Counter Guardian”, in order to save the planet. He agrees. Later on, he finds out this deal requires him to kill large numbers of people to who are causing acts of destruction to the planet. Bitter and disillusioned, Archer regrets his younger self's ideals.
A magic object allows Archer to travel back in time in an alternate universe to year 50 and confront his previous self. He has a choice between whether or not to kill this younger self.
Killing Shirou Emiya does not change Archer's past, but it does stop his alternate, younger self from a life of unimaginable pain.