99% of clubs are 'small clubs' in the sense that they are not in that elite bracket of your Bayerns, Madrid, Barca, Utd. This is like wondering why a billionaire can't relate to a family on average wage. In my experience there is a sense of entitlement that you get from some supporters of the 'big clubs' that you simply do not get at other clubs. Every supporter lives for those moments of glory - for Utd it would be a league win, for Carrick Rangers (as an example) it would be promotion or a win over rivals. We all have our goals for the club we love and they are within the reality of the situation of the club and our expectations are shaped by that. Big club supporters 'expect' success, other clubs 'hope' for success. This is why some supporters of 'big' clubs can't handle it at all when their club doesn't win stuff.
This is it for me. I support a second-division team (Eerste Divisie) in my home town in the Netherlands and had a season's ticket in the 90s. Back then, there was no relegation from the second division, and my team had zero chance of ever making it up, so there wasn't really anything big to hope for or fear. But none of that bothered me. There are no stand-out teams in the second division: the good ones get their promotion, and those that come down from the Eredivisie are often in an awful state and not above the rest. So every game is winnable in theory, and I would just go to the stadium hoping we'd give it a good go and maybe win it. There was a also a strong local rivalry, but that's just one match a year (I didn't attend away matches) and often included fighting back then (one match we had riot police around the away end), so that was tense (I'm really not a fighter myself) and not really about the football.
What I find weird is when fans of really big clubs try mocking me with stuff like "you're a seller club", "your trophy count is empty" etc. I mean, it's not like you've won those titles for your club yourself, did you? So that's nothing to brag about. I mean, you don't really choose your club, you just support it. And such stuff almost sounds as if people chose to support Bayern/United/etc. because they're successful, not because they just grew up like that.
And then they call other fans of some clubs 'plastics' - while clearly their club's trophies play a big role in their own self-esteem. I don't see much difference. I mean, I get the trophy rivalry between United and Liverpool, but if fans of those teams start laughing at, say, Bournemouth for not having won anything...