Eh I don't agree with that.
Wolverine is possibly the most family man of the X-men. The tough love uncle of the team. He's loyal to the X-men
He vouched for Psylocke during her entire Asian body thing.
He's trained sidekick characters like Armor, Kitty, and Jubiliee.
During New X-men, he pretty much vouched and supported most of the characters. I mean no one else ran after Scott after his affair got out.
He was willing to create X-Force and do Scott's dirty work because at that time he believed in Scott and even continued to run it with Angel because they both felt it was needed for the team.
Even before the Schism he was behind Scott and in Consequences he wasn't exactly judgmental of Scott though everyone's frogetten that.
Yeah as far as the X-men would go, maybe a team player isn't the right word, but he's pretty loyal and carring for people. Hell he even seems to be ok with Gambit. He may be his own man, but I don't know about loner. He didn't seem to be that much in later 80s stories. Just the tough dude.
Thats the only reason I don't seem him being on the Avengers. Because he's pretty loyal to the X-men and while he's a part of that team, he's not afraid to make the hard choice when it comes to things. I don't see him as a heroic figure.