The reason why Joe needs to feel powerful is because he is afraid of being an ordinary man. He is overprotective of Janie and treats her as a trophy wife rather than his equal. He claims her as a special privilege that no other men can even look at, evident in his thoughts that "She was there in the store for him to look at, not those others" (55). Notice that Joe only really needs her for managing the store, looking at her, and showing off. Never does he spend time cultivating their relationship. Instead, he lets his ego overpower and stifle any attraction they had for each other when they first met.
When I first read the passage in which Joe buys the suffering mule from Matt for five dollars, I thought this was cute. It seemed like Joe does this for his wife after hearing her mutter that the mule should be left alone and the others should be ashamed of themselves for making him suffer. However, after reading to the end of chapter 10, I'm suspicious of Joe's motives. It seems more realistic that he buys the mule in order to heighten his sense of greatness. I highly doubt he would have thought of freeing the mule without hearing Janie feeding him the idea by accident. Joe capitalizes on every single opportunity to make himself seem like a perfect mayor, similar to the passage in which he turns the lighting of the first street lamp into a grand festivity.
Furthermore, the reader witnesses Joe's extreme sensitivity even at the slightest hint of imperfection. Even though Steve Mixon was merely teasing Janie for cutting his tobacco off the mark in jest, Joe's reaction was explosive. Clearly, he accepts nothing less than perfection, and due to his sensitive ego he is unable to tolerate even harmless jokes about the Starks' store not being competent. However, he only succeeds in exacerbating this ultimate humiliation when Janie insults him in front of the entire store about his aging appearances, revealing his deeply seeded insecurities.
Notice Joe's bewildered thoughts after Janie insults him: "Joe Starks realized all the meanings and his vanity bled like a flood. Janie had robbed him of his illusion of irresistible maleness that all men cherish, which was terrible...she had cast down his empty armor before men and they had laughed...there was nothing to do in life anymore. Ambition was useless" (79-80). The powerful language Hurston uses to describe Joe's chagrin struck me. Saying that "his vanity bled like a flood" goes to show that Joe's pride is his blood and his reason for living. Rendering his "maleness" merely an "empty armor" illustrates that Joe is much too focused on maintaining his manly facade to actually realize that he is living an empty life. He is so dependent on his reputation that he simply gives up and cannot recover after his pride is shattered.
Moreover, Joe's dialogue right before his death further reveals his insecurities and fears: "Janie! Janie! don't tell me Ah got tuh die, and Ah ain't used tuh thinkin' 'bout it...Shut up! Ah wish thunder and lightnin' would kill yuh!...All dis tearin' down talk!...Git outa heah" (86-87)! Once again, Joe breaks out into hysterics and cannot stand the thought of dying. One of the main reasons why he is unwilling to die is because he is unwilling to leave his life with a stained reputation, thanks to Janie. Even at the end of his life, he is unwilling to reconcile with Janie and refuses to hear any criticism of himself. Joe simply cannot acknowledge his own flaws because he is so used to everyone yielding to his demands.
I think the picture is self-explanatory. Since Joe feels the need to constantly place himself above others, he is arrogant.