.. it's because of the traditional 'identity' argument. your club represents your city, your environment, and hence, in some very vague and almost unrelated way, you.
my father is from the same region as Anzhi Makhachkala, the now-ultrarich club competing in the Russian league. i've grown up abroad and have yet to visit due to the volatile political situation, but i watch them whenever i can and support them as fervently as any local fan when they play a Muscovite team. they represent my people in a way, and i'm proud of them.