The naive are the ones who take him at face value and say "Oh look, a horrible psycho." People like yourself. Then we have the "He killed Johnny boo hoo hoo!" people. When I first played GTA 5 the day it came out, Trevor seemed every bit as terrible as you describe him. That's because I took him at face value. As the story went on I learned that he is a mentally-disturbed individual who was molested and abused in his youth and his coping mechanism (drug addiction) has only fueled his rage and bitterness.
Trevor is not a sinner, he is a tarnished saint. He had potential to be a decent human being but circumstances throughout his life shaped him into the maniac he is today. He is a deeply-flawed individual far moreso than Michael. Trevor is a textbook example of someone with Borderline Personality Disorder. He has a fear of abandonment (so he forces people to stay around him), his emotions are out of control, he's prone to reckless behavior and has Intermittent Explosive Disorder (which is often comorbid with those types of illnesses). If you really want to argue a protag with a lot of problems, try Franklin. Franklin is a manipulative psychopath who uses Michael and Trevor to get rich and really has no qualms killing either if you choose A or B. But at the same time, there's a phone call between Frank and Amanda where he says that Michael misses her. This guy doesn't care up until that moment and now suddenly does. That's an out-of-character moment. That's a problem. Same thing with Lamar. Franklin really doesn't care that much and then suddenly does. He even calls and asks Lamar to assist him fighting Merryweather and the FIB just so he can use him for extra manpower regardless of if he lives or dies.
My only problem with Trevor is the By The Book mission. That was unnecessary and poorly-written, thrown into the story just to please the lunatic minority who like torture porns.
Michael is a typical narcissist, by the way. It's all about him and only him. So we have Borderline, Psychopathic and Narcissistic characters to choose from. None of the three are sane.
I don't know if my post sounded like I like any of the characters in the game because every single character sucks. Nothing in the story pulls me as much as the earlier GTA's did. Trevor is worst of the trio. (And by that I mean that he is still better than the rest of the sh*ty cliche cast). He feels as if they watched a bunch of movies about psychopathic people then started adding as much random sh*t as possible "Lets make him a rapist", "lets make him a cannibal", "how about adding mother issues". I guess that they succeded on making a "GTA player" if the players of GTA Online is any indication.