Because Walter Mitty is so weak and hen-picked in his real life, he develops a fantasy world in which he is active and many times a hero.  Putting himself in front of a firing squad would initially be contradictory to his usual daydreams; however in this particular day dream, he plays the part of a noble hero who is put innocently in front of a firing squad.  This may also reflect his feelings about how he feels in his relationship with his wife.  She nags him constantly, and he silently endures.  It is also significant that his daydream about the firing squad comes right at the end of the real day he is having with his wife.  As he is standing on the street, he imagines himself smoking a cigarette bravely facing the firing squad whereas in reality he is standing in the rain waiting for his wife to return from the drugstore.  He knows he is likely to get more nagging the minute she returns.

In "The Secret Life of Walter Mitty," why does Walter Mitty imagine himself facing a firing squad?

Walter Mitty's daydreams are inspired by what is happening in his real life. For instance, when he is driving his wife to an appointment, he daydreams he is commanding a crew flying through a dangerous storm. At the end of the story, Mitty's wife suspects something is wrong with him and says she is going to take his temperature when they get home. The implication is that she is going to start to question him about his behavior and may try to get him to reveal his daydreams. This would signal the end of his imaginary life because his wife would want him to give up his fantasies. So, as Walter waits on the street for his wife to buy one more thing, he daydreams he is in front of a firing squad. He is saying, in effect, I'll never give up my daydreams, even if they kill me. In fact his last words to himself are courageously-—"Walter Mitty the Undefeated, inscrutable to the last."