Back when I was a kid the Narnia series was my absolute favorite. It was fun, magical, and the Pevensies were my favorite. But something always bothered me.
What drove Peter to spare Miraz in their duel?
Peter challanges him to find time for Lucy, and beats him. He doesn't beat him to death with his fists, but turns his back. Then Miraz attacks him. Peter manages to evade the strike and delivers a critical blow. At this point in the fight, he has every right in the world to finish Miraz off then and there. Any code of honour has been disregarded, Miraz has clearly shown contempt, and the fight was to the death, anyways.
Miraz is on his knees, vulnarable to Peter's mercy. There is no reason he should not execute him. He has probably done it before as High King. He has no moral qualms about killing Miraz, either; it is not as if he holds kings and queens in higher regard, as we can see when he waltzes in to fight Jadis. If you watch Edmund closely, you can see him expecting Peter to kill Miraz. "Not the time for chivalry, Peter!" Furthermore, our High King tells Edmund beforehand that he doubts the Telmarines will keep their word. He was prepared for this betrayal.
So why doesn't he kill him? My suspicion is that he wants to test Caspian.
At this point, Aslan has not shown up yet. The two have a shaky relationship, which is further damaged by the debacle at the castle. They are allies, yes, but Caspian is still a Telmarine. One who has shown once already that to him, revenge is more important than the plan. And Peter has been High King for decades; he is intimately aware of the court politics that led to Caspian being by his side instead of opposing him. There has not yet been a time where we see him fight for the Narnians instead of for himself.
Peter wants to know what kind of man Caspian is.
Will he kill the man who raised him in cold blood? Will he let his need for revenge trump his reason? Or will he keep his cool and understand that Miraz no longer needs killing?
By every means, this is a test: a test to see if they can leave their kingdom to Caspian, if Narnia will be safe in his hands. Is Caspian an honourable man? Does he truly care about Narnia? Or will he be a despot? A Telmarine like all those before him?
Playing into this is also the fact that Peter just won't know how Caspian would react if he just kills Miraz in front of him. Their relationship here is not the best. What's the etiquette for killing your friend's abusive adoptive father? Peter killing Miraz himself might make Caspian mad, and he doesn't want that on the brink of their most important battle.
What further complicates the equation is that Edmund, being the diplomat that he is, has undoubtedly picked up the tensions between Glozelle, Miraz, and the other general. He knows they are plotting something. He has shared this with Peter as well, of course.
He says that "Miraz's life is not his to take", but underneath that is a calculated risk. He knows that there is a high chance they will have to fight the Telmarines. He is ready and prepared for it. He also knows that Miraz will likely not survive the ambition of his generals.
What he doesn't know is if he can trust Caspian at his side, send him to lead his troops.
Caspian passes the test. He does not kill Miraz, overcoming his own hatred against him for the good of Narnia. And never again do we see Peter doubt him. They are close brothers after this fight.
It is a very clever piece of writing, and I love the producers for it. It shows so clearly that no, this isn't a 16 year old boy, this is the High King, an extremely skilled warrior, a brilliant tactician, and a clever diplomat. All of it in one scene.
