Two different relationships with the sport
A fan who follows one team closely across a season builds a kind of knowledge that cannot be replicated from the outside: the personnel quirks, the injury history, the small tactical tendencies that only become visible through repetition. That knowledge is deep and narrow, and it comes with an emotional stake that shapes how every close call gets interpreted.
A fan who follows the league broadly builds a different, wider kind of knowledge — comparative judgement about which schemes are working across many rosters, which trends are spreading, which officiating patterns are consistent across games rather than specific to one team's grievances. That knowledge is shallower on any single team and more useful for judging the sport as a whole.
Where the arguments come from
A great deal of online disagreement is not actually a disagreement about facts; it is two different modes of following the sport talking past each other. The team-focused fan is arguing from inside a season-long emotional narrative; the league-focused fan is arguing from a comparative, detached vantage point. Both are legitimate ways to watch football, and both produce real insight the other one misses.
Recognising which mode a conversation is happening in would defuse a surprising number of arguments before they start, because a complaint that sounds like homerism from one angle can be a genuinely well-supported observation about officiating trends from the other.
There is room for both
I do not think either habit is more legitimate than the other, and I would resist anyone who tries to gatekeep fandom based on which one you practise. The sport is large enough to support people who know one roster intimately and people who can compare forty years of scheme evolution across the league, and the conversation is richer with both in it.
What helps is simply being honest about which lens you are using in a given argument. Arena's NFL guides are built for the second kind of fan, but they are just as useful as background reading for the first.