The hardest of hearts is the heart that used to love, and has since turned to something more like hate. Not quite hate though, because there is still love there despite everything. It's that lingering shred of love that hardens a being so, because they wish with all that they are that they did not love. They wish for hate, and anger is stirred up in its place, because love makes hate impossible.
Anger though, that can be used. It burns hotter than a forge, tempering Michael and his traitorous heart into nothing more than cold steel and righteousness. He loves his brother - more than anything - and that's why he must kill him.
This way, Michael can look back and remember Lucifer as he was. He can love him without the anger that threatens to overwhelm him in the place of the hate he should hold for this monster, this abomination.
"You did it to yourself," He tells his brother, not wanting to hear how their father has planned this, because to harden himself against their father now... He can't bear this same knife in his chest again. He refuses to admit that it makes him a coward.
Michael doesn't want another truth. It's so much easier to kill his brother and pretend that it solves everything, because if he does, it will.
Still, Lucifer's voice whispers to him like sweet deception. "He made me this way. He needed a devil." And it's true, but Michael can't hear it. He needs to see his brother the way he did before the fall, when Lucifer was a shining bundle of light and possibilities, looking up to him like Michael held the universe in his hands. That is what Lucifer deserves to be remembered as.
Michael loves his brother, which is why he must stop him. Because he wishes he could hate this thing Lucifer's become. Because he doesn't want Lucifer to be right, after all. He can't have chosen the wrong side, because he can't.
He can't have hurt his brother, can't have turned away when Luci needed him the most if he's still Michael's little brother - the angel he loves most of all.
Because then it's him who's been betrayed.