How does Colonel Sherburn justify shooting Boggs?

I do not really think that Colonel Sherburn ever comes
straight out and says why he has shot Boggs.  Instead, we have to infer it from what he
does say before and after.  From that, we can infer that he shoots Boggs to prove he is
a man -- he shot Boggs because Boggs insulted him and a real man does not stand for
that.

We can see this first before he shoots Boggs.  He
tells Boggs that he will not stand for his insults past 1 PM.  We can see it later when
the men come to lynch Sherburn.  He tells them that they are not men while he
is.

Between these, the implication is that men fight back
when they are insulted.  Boggs has insulted him and questioned his bravery and since he
is a man, Sherburn has killed Boggs.