As Cole's parole officer, Garvey seems to be the only person in his life who continues to believe in Cole and is persistent in getting him to see his mistakes and change. At first, this kind of tenacity annoys Cole, and he constantly lashes out at Garvey and tries to get him to go away already:
Cole couldn't figure Garvey out. He knew the probation officer was super busy, so why did he visit so often? What was his angle? Everybody had an angle—something they wanted. Until Cole could figure out what Garvey wanted, he resented the visits—he didn't need a friend or a babysitter. (1.32)
But Cole's lucky to have someone like Garvey in his life. His parents haven't exactly been there for him every step of the way, and it's good for him to have an adult who is willing to fight for him…even if he doesn't realize it at first. Garvey is the one who gets Cole into the Circle Justice program because he believes Cole can still be saved and shouldn't go to jail where he'll just become a hardened criminal.
Later on, Garvey reveals that he keeps giving Cole second chances because he was once a troubled youth, too, and he wishes someone had seen the good in him the way he sees the good in Cole. That's why he and Edwin want to help him in any way that they can, even if it means they have to stick out their necks:
"We still believe in you and think there's hope," Garvey said. "Because of that, we've stuck our necks out so far, we feel like two giraffes." (15.59)
By remaining a constant, supportive presence, Garvey gives Cole what he's never gotten from his parents: an adult who believes in him and wants to see him succeed. He's able to see himself through Garvey's eyes, and in doing so, Cole realizes that he's not such a lost cause after all.