Both in- and out-of-universe answers are going to boil down to "character development." However, I do strive for the illusion of professionalism, so strap in.
In-universe
I think we can all agree that Ren massively idolizes Darth Vader; he keeps Vader's burnt helmet in his room, he talks to it, and Rey picks up on Ren's self-comparison during her interrogation:
Rey: You're afraid that you'll never be as strong as Darth Vader.
The Force Awakens (2015)
It doesn't seem like a stretch to say that Ren is trying to model himself off his hero. Unfortunately, he's having a pretty stressful few days; part of his primary goal is the destruction of the Jedi (here meaning Luke), but he's constantly being thwarted by things outside of his control. Considering we know that he's not quite as firmly connected to the Dark Side as he wants to be (or wants to think he is), it's not totally unreasonable to imagine this might provoke some...extreme reactions.
At this point he's still trying to maintain his image publicly, but the mask is slipping; I think we see this most clearly in his face when Hux bursts in on his (unmasked) conversation with Snoke, after failing to interrogate Rey:

It's difficult to convey all of the emotion on display here with a still image1, but Ren is clearly ashamed to have been caught in a vulnerable position.
Once Han enters the equation, things become vastly more complicated; as Ren himself admits to Vader's helmet, and later to Han, there's an emotional trigger there that he hasn't quite purged yet:
Ren: Forgive me. I feel it again: the pull to the light. The Supreme Leader senses it.
[...]
Ren: I'm being torn apart. I want to be free of this pain; I know what I have to do, but I don't know if I have the strength to do it.
The Force Awakens (2015)
However, at this point Ren makes a decision: he chooses Snoke and the Dark Side; by all accounts, this is Ren's Moral Event Horizon2, as Snoke implies earlier in the film:
Snoke: Even you, Master of the Knights of Ren, have never faced such a test.
The Force Awakens (2015)
So now he's one step closer to being the 'lil Vader he always dreamed of. His internal conflict resolved, Ren is now free to return to kicking ass and chewing brightgum.
Out-of-universe
In an interview with Entertainment Weekly, Abrams mentions that he wanted the villain to be still-forming:
"Long before we had this title, the idea of The Force Awakens was that this would become the evolution of not just a hero, but a villain," Abrams said. "And not a villain who was the finished, ready-made villain, but someone who was in process."
So what we're seeing is literally Kylo Ren's Villain's Journey, or at least the last stages of it; we can actually compare several known events in Ren's fall to Joseph Campbell's stages of the "Hero's Journey", though with inverted morals:
We meet Ren in the middle of "The Road of Trials"; he's committed to his path, but he's still learning; Snoke tacitly admits at the end of the film that Ren's training is incomplete:
Snoke: Leave the base at once and come to me with Kylo Ren. It is time to complete his training.
The Force Awakens (2015)
As hinted in some of the quotes above, Han Solo (and Ren's lingering familial love for him) clearly represents "Woman as Temptress" - which need not necessarily be a literal woman
Ren and Han's final encounter represents the "Atonement with the Father"; Campbell's own description of this stage fits it quite well:
Atonement consists in no more than the abandonment of that self-generated double monster [...] But this requires an abandonment of the attachment to ego itself, and that is what is difficult. [...] The problem of the hero going to meet the father is to open his soul beyond terror to such a degree that he will be ripe to understand how the sickening and insane tragedies of this vast and ruthless cosmos are completely validated in the majesty of Being. The hero transcends life with its peculiar blind spot and for a moment rises to a glimpse of the source. He beholds the face of the father, understands—and the two are atoned.
The Hero With a Thousand Faces
Following the "Atonement", Ren experiences the beginnings of "Apotheosis", the state of Divine Knowledge that arises from conquering his self-doubt
Narratively, Abrams is trying to make us connect with Ren on a somewhat deeper level than we would with the typical moustache-twirling villain. The implications this has for the remainder of the films, of course, remains unclear.
1 And I've not quite mastered capturing GIFs from my screen
2 TVTropes link; all hope abandon etc.