Subaru, despite all appearances to the contrary, does not want to kill Seishirou. Nor, by the way, does he want Seishirou to kill him. Rather, what he wants is for Seishirou to not kill him.

Not that that's as simple as it seems. Subaru wants Seishirou to be unable to kill him, to be incapable of killing him. Subaru lives for each time he can walk away from a fight, because it's one more time that Seishirou was swayed by the emotions he refuses to acknowledge.

Subaru knows he wouldn't be difficult for the Sakurazukamori to kill, if only because he's never tried. He doesn't want to beat Seishirou. It's only meaningful if it's Seishirou's choice that Subaru lives. Subaru works hard to be just a little worse a fighter than Seishirou is.

Subaru wants Seishirou to let him live. To Subaru, it's as good as saying "I love you."