How can she possibly draw strength from someone as broken as him? It must be because she's Rin Tohsaka, and once she sets her mind to something, impossible things aren't impossible any longer.

Archer's hand stays on her head; his fingers stroke her hair.

"That's fine. This is a rotten world and it's best if the few bright things in it don't burn out. You're the brightest of them, so I'll shield you especially."

He's smiling now as he speaks. How stupid of him to take so long to realize it: protecting Rin above all makes perfect sense when he puts it like that.