To answer this question, it is important to consider it from different perspectives. From the perspective of the rebels, for example, killing Captain Torres would make the barber a hero. This is because the captain has killed many of their comrades and, as a result, they view him as their enemy. At one point in the story, the barber alludes to this heroic status when he is considering killing the captain:
"And then on the other side. "The avenger of us all. A name to remember. (And here they would mention my name.) He was the town barber. No one knew he was defending our cause."
In contrast, some people, like the captain's men, might call the barber a coward for killing Captain Torres. After all, only a coward would kill an unarmed man while giving him a shave. At the end of the story, the captain appears to judge the barber as a coward when he reveals that he knew he might be killed:
"They told me that you'd kill me. I came to find out."
So, in an ironic twist, the captain views the barber as a coward, even though he has, in fact, saved his life.
The decision that the barber has to make will either result in him being regarded as a coward by the rebels and a hero by the military, or a coward by the military and a hero by the rebels. Consider how he balances the way that his actions will impact his future and how others will think of him:
"Captain Torres' murderer. He slit his throat while he was shaving him--a coward."
And then on the other side. "The avenger of us all. A name to remember. He was the town barber. No one knew he was defending our cause."
Therefore we can see that the two opposite reactions depended entirely on the people that you are talking about. The rebels would have considered the barber a hero, whereas the military would have hunted him down like a dog and killed him for a coward. The barber finds himself in an immensely difficult situation, where acting or not acting is going to have massive consequences on the rest of his life.