When Castiel was ruled over by higher powers and was an emotionless angel, he did not care how he impacted the lives of his vessels. As he grew, though, he grew more conscious about how he affected and even ruined the life of Jimmy Novak's daughter, Claire.
Cas hated how Claire hated him and desperately wanted to make things up to her.
He also grew protective of her, acting like somewhat of a father figure in attempts to protect Claire from the dangers of hunting and the general dangers of being out in the world alone with no parents - which is not just out of fear from Cas, but guilt too. When Claire found Jody and the Wayward sisters, these fears were somewhat diluted, but Cas still felt responsible for Claire, similar to Dean and Sam.
While Castiel did leave behind his bosses and the corruption of heaven to fight for humanity, the planet Earth, and free will, he still cared about heaven.
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