You became an Eva pilot. You are a minor so you need a care taker. Misato already has Shinji and Asuka, Kozo decided to take care of you because why not. He didn't see anything against it, he had nothing against children. Especially since you seemed calm and quiet

When he brings you to his apartment he lets you in. It's a rather clean and tidy apartment.

Kozo: This is it. Want to see your room?

He asked with his calm and serious expression on his face.