The ostensible purpose of a duel is to restore honor (I'll use the American spelling since we are talking about the USA), not to kill your opponent.

The participants are presumed to be gentlemen, or men of honor, otherwise the duel would be an inappropriate charade that risked bringing disrepute on the custom. Common, or low, men were presumed settle their disagreements with fists or knives or cudgels or some other scrap unregulated by the conventions of high society and good manners. Such men could not be trusted, it was felt, to maintain the high decorum of an affair of honor. For these and other reasons, it was quite acceptable to reject a challenge from someone who was significantly beneath your station, with no risk to your own standing.

The duel itself was not like a wild-west gunfight, in which you tried to drop your man by any means possible. It was more like a game of Russian Roulette: bullets were going to fly in a rather dangerous manner, but the more random and unpredictable the outcome the better. This is because the ritual existed to prove one thing: that the participants valued their honor more than they valued their life. They were not just proving it to each other, but to witnesses and to society. A deadly ritual that relied on skill to murder your opponent before they murdered you back could be abused for vendetta purposes (and, frankly, duels were frequently abused for just this purpose). Part of the appeal of pistol duelling was that it emphasised luck over skill in a way that sword duels did not. Pistol duelling conventions actually sought to increase the role of luck in various ways, such as by drawing lots to see who would shoot and who would receive the shot.

So it went like this: you and your rival had a serious disagreement that one of you felt brought dishonor upon him, and for whatever reason (pride, obstinacy, protestations of innocence, whatever) apologies or reconciliation were impossible to extract, and therefore honor was irreparably damaged. Satisfaction (recovery of honor) could only be achieved through violence. But simply agreeing to murder each other in a controlled fashion was not genteel, so instead an elaborate game was constructed. If you both sincerely felt that your honor prevented you from resolving the dispute politely, and since as gentlemen your honour is more valued than your lives, you both agreed to put it to the test. You will both face death, and that will prove to each other and to witnesses that (A) you are truly men of honor, and (B) that your dispute is sincere. Only then would reconciliation be possible.

Reconcilation or death, basically. But they were quite serious about the death part.

The prescribed number of bullets fly. Small chance that one of you dies (only a few percent chance in the late 19th Century, higher the further back in time we go). If you both live, reconciliation now becomes possible because the looming possibility of death has given you new respect for your rival's sincerity. If not, well, at least there was death with honor, which was what was missing when the affair began.

That was how it was supposed to work, in theory. In practice, it was often a much more sordid and corrupt affair. The inability to manage the sordid aspects of duelling eventually contributed to the death of the custom. But if you presumed to engage in an affair of honor, you would have to grant your opponent a fair chance to shoot you down under the agreed upon rules. That was the whole point. Dodging would have demonstrated the opposite - that your honor was worth less to you than your life, that you were unfamiliar with the standards of behaviour of a gentleman, and that you were entirely unfit to be participating in such an affair. Rather than grant you the honor of standing in front of your gun, I should have just caned you in the street like the worthless ruffian you are.