kakashis store was left to him by his father, he never really planned on keeping it but then these punkass high school kids decided they needed a paycheck and he ends up hiring them so now hes got these kids AND a shitty store to watch over

gai opens his store a little after kakashi takes over his so CLEARLY they are rival stores now, its in the rules kakashi, i dont write them i just follow them!! gai’s family friends has a son who absolutely adores him so gai hires him to work part time at the store, and lee ends up bringing along his friends to work as well because gai needs the help

aside from gai, lee and naruto are the only ones who ever get caught up in the rivalry thing mostly because its so easy for naruto to get competitive, they stand outside their stores yelling at people to come shop inside but then just end up shouting at each other from opposite sides of the road. business was SO BAD that day.