The point of view of this short story is first person. The barber is telling his own story.
This affects the story because it gives us great insight into the major conflict of the story. The major conflict of the story is the dilemma that is going on inside the head of the barber. He is having to decide what to do about this man who is really an enemy to him. He holds the enemy's life in his hands and must decide what to do.
By using a first person point of view, the author lets us see quite clearly all the tension that goes on in the protagonists mind and all the things he must consider.
The short story "Just Lather, That's All" is mainly an interior monologue, a technique of narration that presents the thoughts that pass through the mind of the protagonist. This interior monologue occurs in first-person narration.
While interior monologue is often used to exhibit loosely related associations of thought, it can also be composed, for instance, of rational and structured sequences of thoughts and feelings.
Such is the case of the barber, whose thoughts are, indeed, rational and structured. As he prepares to shave the man he recognizes as Captain Torres, the barber ponders his dilemma: should he kill this man who is his enemy, or should he shave him? The narrator decides he will be the barber first and the revolutionary second because he has worked hard at his profession and he takes great pride in his skills.
Thinking he has resolved his conundrum by deciding to just shave the man skillfully and retain his pride in his profession, the narrator is surprised to hear Torres say,
"They told me that you'd kill me. I came to find out. But killing isn't easy. You can take my word for it."
His ego deflated, the narrator abandons his interior monologue in which he has prided himself on his deception and restraint, and he simply adds, "And he headed on down the street." This abandonment of the proud interior monologue signifies that the machismo of the barber has been deflated.
The short story "Just Lather, That's All" is told through the first person narrative which is narrated by the barber. By having the barber tell the tale the reader is able to step into the barber's experience as he contemplates what he should do. The reader feels the tightening in the throat and the tension of one's body as one follows the thought process of the barber. One can almost feel one's own hands becoming sweaty and shaky while the barber is shaving the man and contemplating slitting his throat.