The barber eventually comes to the conclusion that he will not kill Torres because he discovers something very central about himself, his identity, and what he can and can't do. This epiphany also recognises something central about the identity of Captain Torres. Note what the barber concludes as he makes his decision not to kill Torres, in spite of what he had done and what he will continue to do:
But I don't want to be a murderer, no sir. You came to me for a shave. And I perform my work honorably... I don't want blood on my hands. Just lather, that's all. You are an executioner and I am only a barber. Each person has his own place in the scheme of things. That's right. His own place.
The barber recognises that, to him, what is most important is honour. As a barber, it is vital to him to do the best he can in his work and job, which means giving the best shave he can. He also recognises that "each person has his own place in the scheme of things." Even though the place of Torres is clearly to kill and murder, that is his place, just as it is not the barber's place to kill. The identity of Torres is defined by his being "an executioner," whereas the barber's identity is defined by the job that he does. The barber therefore decides not to kill Torres because he realises that this is not part of his central identity.