Kylo and Rey are not brother and sister, but Kylo desperately wants them to be. In fact, he even believes she is his little sister. He theorises that she was born in secrecy (for whatever mad reason he thinks up) and was obviously hidden when he started turning to the dark side.

He just wants a sibling. Someone who he can teach the ways of the dark side to, but also love and protect. Lots of him trying to dote on her while she's just desperate to get away.