Carl Jung developed the concept of the "shadow" or "shadow aspect" (of the psyche). As reference, per
Wikipedia the shadow is the "unconscious aspect of the personality which the conscious ego does not identify in itself. Because one tends to reject or remain ignorant of the least desirable aspects of one's personality, the shadow is largely negative."
Some quotes from Jung:
"Everyone carries a shadow and the less it is embodied in the individual's conscious life, the blacker and denser it is."
On the tendency of the shadow as projection: "The projection-making factor (the Shadow archetype) then has a free hand and can realize its object--if it has one--or bring about some other situation characteristic of its power."
Generally speaking, the shadow has negative energy, although Jung thought it could also be the "seat of creativity."
All of that applies directly to Whiplash. How? Think about this: Fletcher as a physicalized projection of Neimann's shadow.
Neimann's drive to be the best. His need to feel superior to others (witness the awkward dinner conversation with his extended family). His self-abnegation. Driving himself to bloodied hands. That is all a part of Neimann's psyche.
Fletcher embodies all of that energy as a superior and external figure.
Fletcher is the projection of Neimann's shadow.
Now there are other parts of Neimann's psyche. His attempts at a relationship with Nicole demonstrates he would like to be in love. He's kindhearted toward his father, even if he probably thinks of him as pretty much a loser. He has a passion for music and an affection for creativity.
However his shadow bends and shapes all 'positive' aspects of his psyche through his obsession.
If we step back from Neimann's story and ask this question - Why does THIS story HAVE to happen to NEIMANN at THIS time - in my view, it boils down to this: He needs to confront his shadow self in order to determine who he is. That's why the universe intersects him with Fletcher, why Fletcher decides to work with him, and why they enter into their decidedly unhealthy relationship.
Given that, consider the end. Fletcher has set up Neimann to fail in such a way, Neimann would have no future as a jazz drummer. As spiteful and meanspirited as that is, in one way of looking at the story, that is the ONLY chance Neimann would have to go on and have a healthy psychological life. He could walk away from his obsession, be freed of its claim on his soul. And he ALMOST does.
But then he comes back. And while what he does is amazing, achieving a level of drum- playing he'd never hit before... while he proves to himself he can do it... while he wins over Fletcher...
He is doomed. Chazzelle himself said as much -- I can't find the article, damn it! -- when he was asked what he imagined happened to Neimann after the end of the movie and Chazzelle said he thought Neimann would be dead by the age of 35. Just like Sean Casey, another of Fletcher's students who had not died in a car crash, but committed suicide.
So in sum, I see Neimann's psychological journey as one where he confronts his own shadow - in the form of Fletcher - and rises to the level of his obsession, achieving a perverse sense of unity, one that will ultimately destroy him.
That's my take. What's yours?