Conor wasn't always isolated, but he's definitely hopped on board the lonely train since his mom got sick. Not only do her treatments take her away from him, but his classmates and teachers are ignoring him so as not to set him off. Nobody knows what to say to him in the face of a dying mother, because most of them haven't experienced it. He becomes an outsider, a "them" in the mindset of "us and them." Sometimes when you don't know what to say to someone, it's easier to say nothing at all. Yet A Monster Calls shows us how harmful that tactic can be.
One reason Conor called the monster is so that he'd have someone to talk to; someone who actually sees him. The monster may be a monster, but it gives Conor its full attention.
Conor needs the monster to give him the courage to do highly visible things, like wrecking his grandma's place and giving Harry a beatdown. Only by believing the monster is responsible is he able to carry out his actions and get noticed.