Quote 1
Cole felt a sudden rush of anger and jerked away. Why did everybody always have to touch him? He didn't need anyone's help. What he needed was for the world to butt out. "Aren't you guys ever leaving?" he snapped. (2.41)
Edwin and Garvey are the first people who are truly nice to Cole, but instead of appreciating it, he pushes them away. It totally weirds him out that they're invested in his well-being.
Quote 2
On Christmas Eve, Cole sat alone in front of his twisted little tree as the wind outside moaned through the treetops. Did anyone anywhere miss him at this moment? He went to bed early that night, not knowing the answer to that question.
The next time Edwin visited, Cole said to him, "Christmas was really lonely. I feel like the whole world has forgotten about me." (24.27-28)
Cole's gotten somewhat used to being alone on the island, but spending Christmas all alone is still pretty depressing. Even cutting down his own Christmas tree and making ornaments out of foil doesn't raise his spirits.
Quote 3
Cole turned to face the wall. "He drinks until he turns into a monster. Mom just gets drunk and pretends nothing has happened. It's like a bad dream I can't wake up from." (3.17)
There's no lost love between Cole and his parents. When Garvey asks about them, he tells him the truth: They've never been there to support and love him, and they've always been a negative force in his life.