Finn's problem is that he can't seem to hold onto anything. His dad. His best friend. Rachel. Quinn. Now that he's graduating, the team and the glee club will all be gone, too. And without getting into that acting school, Finn knows he has nothing else to lose. After all, it was this that he wanted all along.
An opportunity to do something for his dad.
He has that habit, he guesses, of chasing things he has no chance at ever getting. But he has to try. Even though his mom is afraid for him, more than anyone, because she knows what this did to his dad. This gives Finn a purpose and a drive that he hasn't had in…well…ever.
He can play drums but that won't get him anywhere in life. What he can do - what Finn has always been able to do - is be a part of a team. Whether it was football, or glee club, Finn gave it his all, and he did his best. And maybe he hasn't always made the best judgment calls, but at least, if he does this, Finn can put his best skills to use.
And maybe, instead of turning out like his father, he'll come home the person his father can be proud of.
That's all he really wants.
The End.