Part of the reason Becket's characterization is so appealing is that he shows the pliable and fluid nature of human identity. Unlike Henry, Becket shows that a necessary part of human identity is change. This metamorphosis is how Becket sees his own life, and is a world view that Henry does not change. When confronted with how Becket's notion of self has transformed his view of the world, Henry strikes with venom in his tone:
Yet I know you well enough, God knows. Ten years we spent together, little Saxon! At the hunt, at the whorehouse, at war; carousing all night long the two of us; in the same girl's bed, sometimes . . . and at work in the Council Chamber too. Absurdly. That word isn't like you.
Henry believes that Becket will always be the "little Saxon" who accompanied him during their hedonistic ways. It is for this reason that he sees Becket as being guilty of betrayal. He sees it as betrayal because he believes that human beings are more plastic, and less likely to change. When Becket responds that he is a changed man, it reflects how further along the path of spiritual growth he is from Henry:
I felt for the first time that I was being entrusted with something, that's all—there in that empty cathedral, somewhere in France, that day when you ordered me to take up this burden. I was a man without honor. And suddenly I found it—one I never imagined would ever become mine—the honor of God. A frail, incomprehensible honor, vulnerable as a boy‑King fleeing from danger.
The critical element in Becket's own sense of metamorphosis lies in "suddenly I found it." For Becket, being able to find this voice and sense of identity is what makes him divergent from Henry's view of being in the world. It is a statement in which Becket acknowledges that Henry will never change. Henry will not change from his world view and Becket cannot change from his. The collision between equally desirable, but ultimately incompatible notions of the good is where both men lie. This sense of resolve in how both men perceive the certainty within their actions is where betrayal is perceived and resolve impossible.