|Film hasn't been invented, yet. Why am I screenwriting?|
Over the course of a well-told story, a flawed, sympathetic, interesting protagonist struggles for what he/she wants more than anything, ultimately changing him/herself or inspiring change in others. Someone, over the course of your story, grows up. Films are, to borrow a phrase from author Philip Pullman, about the transition of "innocence into experience."
However, interesting ≠ likable. A protagonist does not need to be likable. However, if they're not likeable, they had better darn well be charismatic and interesting. And ideally, they've experienced an injustice or loss (i.e., they must be sympathetic). But this does not mean that they must be the nicest person in the room. Oftentimes, they're not.
Some of the best film characters have been anything but likable. The Godfather's Michael Corleone, There Will Be Blood's Daniel Plainview, Casablanca's Rick Blaine, Citizen Kane's Charles Foster Kane, A Clockwork Orange's Alex DeLarge, Amadeus's Antonio Salieri... each of these characters have displayed elements of selfishness and/or violence, but they're certainly interesting and complex.
A good place to start would be to imagine a conversation between two secondary characters about your protagonist. What would they say?
"He's a brilliant composer."
"He is, but his vanity will be his downfall."
Right there, we have two key attributes that lend considerable weight to characterization. A brilliant composer who is his own worst enemy. I'd go even further and say that every protagonist must in some way be selfish. Selfish does not mean dislikable, but by definition, an active protagonist is willing to move heaven and earth to obtain what he/she wants. Isn't that a bit selfish? A protagonist needs to sacrifice to make his/her plans come to fruition, but what if a protagonist, in his/her drive to the goal, ends up marginalizing or hurting others? A truly sympathetic protagonist should intentionally hurt no one other then him/herself, and oftentimes, the great irony of a protagonist is that the further they stretch toward their goal, the more they hurt themselves. In either case, in order to attain his/her goal, a protagonist will have some big decisions to make, and acting on such decisions will show us more about your character than anything you could otherwise tell us.
Some characters are selfish to the end. See Citizen Kane:
Some characters aren't. See Up:
But in both cases, there exist characters who need to make it over themselves. Your protagonist must start in a situation wherein they have a long way to go. Their own internal complexities are what make a potentially otherwise easy journey especially difficult. They might have a worthy antagonist to defeat, but first, they must slay their own selfish natures.