He'd told Rey that she was nobody, but that couldn't be further from the truth.

It'd hurt to say this, and the pain only worsened when he saw the agony reflecting in her eyes. But Kylo Ren had seen where the scavenger came from, and with Rey's linage the potential power she held. If she grew into this potential, there was a good chance she may be able to overthrow Kylo Ren herself.

Kylo Ren didn't want to fight Rey, nor did he want to let her go back to the Resistance. So he'd told her she was no one of significance with parents who'd abandoned her.

Kylo Ren didn't want Rey to know the truth, though he knew one day she would discover her heritage. Still, the search for her parents had been her greatest weakness, causing her to go so far as to jump into the dark pit on Ahch-To. If she believed her parents were long gone she would no longer desperately seek an answer, nor put herself in danger's way. With this greatest weakness gone, she would now be able to move on with her life.

A life, as he'd foreseen in the vision, that would eventually place Rey by his side.