Kylo could see into Rey's head. He could see her memories. His mother loved her. His father adored her. Luke trusted her. All of his family, all of the people that were supposed to support him but had betrayed him, it was she they chose to put their faith in instead.
He wanted to hate her for that. She stole everything that belonged to him, even his grandfather's lightsaber. And yet he could not. Instead, when he looked at her, the idea of redemption even crossed his mind. She made him want to be better. Good. And that scared him.