I am a dummy...

For some reason, I thought that New Spock had no idea Old Spock existed until he met him in the ship docking area and they talked. But tonight, as I was watching youtube clips to research for a fanfic, I realized that on the Jellyfish, Spock inferred that his future self had been in the ship and that Kirk knew about his future self AND that Kirk realized that Spock knew/suspected his future self had been in the ship.

So why is it that I thought that Kirk would still be trying to keep Old Spock...