Except he cared about LOTS of things. He was just lying to himself.
He cared about the dog. A lot. Saying it was just a responsibility was total bullshit, to such an extent even he kind of knew it.
He cared about his Dad. Yes, his visits were posed as really short, and its not like he had to travel far so we don't know how distance would have affected his visits, but I don't care how easy it was, or how short those visits were. They were REGULAR. And with a parent with that condition... that says a lot.
He cared about his photographer friend. Even while mocking him mercilessly, you could clearly see there was love there too.
Even his claims that he'd stripped away all the social conventions was crap. Most of them, yes, especially where there were no consequences, but notice he was never cruel to the new girl. Not even once. He could be cruel without regard to strangers, because of the lack of consequences. He'd usually never have to deal with them again. He could be cruel to those who knew him well, again because of the perceived lack of consequences--in this case because he knew they'd excuse and forgive him. But he couldn't be cruel to someone new to him who he'd have to continue knowing. Someone where, even not by choice, he had to build a new relationship with--and where it was clear she was a really nice person and didn't deserve cruelty. It showed the lie of his claim that he really didn't care. The lady in the cemetery was similar. He CARED what she thought of him.
In a way that was very well shaded and sophisticated writing. Who he treats in what way is a very subtle furthering of the story in how it showed his real character under the outrageous Dickery. So in the end, when we see him change it's not a clichéd Ebenezer Scrooge after his night of Ghosts piece of malarkey from the blue. Because we've seen him show better character traits all along in certain circumstances.