Dave wants to be seen and treated as a man; when others laugh at him, the laughter serves as a harsh reminder of Dave's place as a "boy" in his family, in the fields he works, and in his society. The story's events illustrate Kubler-Ross's five stages of grief (see the link below) through Dave's quest to become a man.
The story's opening paragraph states Dave's reasoning for buying the gun; the gun's function is not as an equalizer but as a threatening silencer:
One of these days he was going to get a gun and practice shooting, then they can't talk to him as though he were a little boy ... Shucks, Ah aina scareda them even ef they biggern me! ... Mabbe Ma will lemme buy one when she gits my pay from ol man Hawkins. Ahma beg her t gimme some money. Ahm ol ernough to hava gun. Ahm seventeen. Almos a man.
Dave's words illustrate his anger but implicate his solution as immature. If the others see him practicing shooting, they will fear him, but practicing implies a lack of readiness. The gun symbolically increases his manly stature—it makes his violent potential greater than the others' physical size. Ironically, Dave cannot hear the boy in his own thoughts—to buy the gun, he will "beg" his mother to give him his money. He is in denial.
He reasons he is old enough to have a gun because he is "almost a man," but when he appears at Joe's store to borrow the Sears catalog, Joe's laughter reminds Dave that everyone in town sees Dave as a boy:
"Your Ma letting you have your own money now?"
"Shucks, Mistah Joe, Ahm gittin t be a man like anybody else!"
Joe laughed and wiped his greasy white face with a red bandana.
To attain the two dollars Dave needs to purchase a gun from Joe (a form of bargaining), Dave exploits his mother's love (using his boyish charm) and avoids his father's dominance: "He did not want to mention money before his father. He would do much better by cornering his mother when she was alone."
Dave purchases the gun through childish means, which foreshadows his childish handling of the gun and Jenny's death—the consequence is laughter from the gathered crowd after Dave's parents and Jim Hawkins publicly confront Dave. Dave tries to bargain:
"Ah wuzznt shootin at the mule, Mistah Hawkins. The gun jumped when Ah pulled the trigger ... N fo Ah knowed anything Jenny wuz there a bleedin."
Somebody laughed. Jim Hawkins walked close to Dave and looked into his face.
"Well, looks like you have bought you a mule, Dave."
... All the crowd was laughing now. They stood on tiptoe and poked heads over one another's shoulders.
"Well, boy, looks like yuh done bought a dead mule! Hahaha!"
The crowd's laughter heightens Dave's sense of futility (depression). When his father threatens and further demeans Dave in front of the crowd—"N don fergit Ahma lam yo black bottom good fer this! Now march yosef on home, suh!"—the crowd laughs at Dave's fate. Dave realizes that in his current setting he will never gain the power or respect he desires: "Hot anger bubbled in him ... he was hurt. Something hot seemed to turn over inside him each time he remembered how they had laughed ... Nobody ever gave him anything ... They treat me lika mule ... N they beat me." The laughter forever marks Dave as the boy who bought a dead mule. His anger transfers into acceptance and action—the fifth stage of grief.
His only way to accept such a fate is to prove his manhood through a final act of violence and emancipation, enacted under the cover of darkness: "with effort he held his eyes open" as he shoots the gun's last round at the edge of the woods. He stands in the moonlight and imagines that if he had one more round, he would shoot at Hawkin's house to scare Hawkins "Jusa enough t let im know Dave Sanders is a man." Dave returns to a state of denial: he can only imagine Hawkin's fear and respect. He jumps on a train to escape the setting where he is a boy for somewhere he can be a man. His action illustrates both acceptance and denial. He is still grieving for an elusive sense of manhood.
Wright uses the empty gun as sexual imagery. Dave's gun is out of ammunition when he jumps the train "stretching away to somewhere, somewhere where he could be a man"; the empty gun symbolizes Dave's impotence—his ongoing fate as almost a man.