Derek had been annoyed by Joy's moping and general lifelessness and had given her a serious case of tough love. He ended up telling her about what happened with his family after finding out what had happened to hers and snapped that Paul wouldn't want her to give up on everything.
He had been right, of course. Paul wouldn't want her to give up on everything.
Slowly but surely, Joy came back to life because her friend forced her to eat ("what, do you want to be a skeleton?") and do something other than stare blankly at the wall when she got home from work ("it's creepy when you space out like that!").
She would always owe Derek for that. He had been harsh but she had needed the harshness at the time. Nothing else would have worked.
Sympathy only made her feel worse. That was another major reason she didn't like talking about her problems. But it didn't matter as much with him because he already knew about them.