The Left Hand of God - or why Peter Hale is Mad, Bad and Dangerous to know by Athenadark is a rather excellent examination of Peter being the left hand of the pack. He's not a good person, but he does tend to act for the survival of the pack as a whole. This meta also makes sense of Peter's actions during season 4 and identifies some of the people that Peter is protective of.

Interestingly enough, I later found out first hand that Ian Bohen also thinks Peter is the left hand of the pack. Granted the opinions of the actors don't necessarily reflect actual canon, but it is interesting when what they think matches up with meta/analysis of canon.

4x12 Smoke and Mirrors

Scott: You taught Kate. You helped her.

Peter: All for power. For my family's power. To be rightfully inherited by me. Not usurped by some idiot teenage boy, so incorruptible, he won't shed the blood of his enemies even when justified. You don't deserve your power. Not power like this.

...

Peter: You were my Beta first, Scott. It was my bite that changed your life. And my bite that can end it.

Scott: Then, end it, Peter. Because you won't get another chance.

Peter: Come on, Scott. Come on! Come on. Fight like an Alpha, Scott. You want to defeat me? You're going to have to kill me!

The thing is, although Peter goes to extremes, he is right. Scott's dad pointed it out to Scott earlier in the season that sometimes killing is necessary and justified in order to protect people. Sheriff Stilinski also points it out in season 6B. Being an alpha comes with responsibilities and one of those is that you need to be willing to kill threats to your pack (and the rest of the town) before they kill you. Peter is trying to force Scott into realizing this. He demands that Scott fight like an alpha to prove himself worthy of the position. Peter goes to such extremes because he already had to deal with Talia not acting against the Argents which resulted in his pack being decimated in the Hale House fire as well as his own agony from being burned and driven insane while trapped in a coma for six years.