So your Father was a Manchester United fan.
Your Brother a Sunderland fan
You are an Arsenal fan.
How strange that you all followed different teams. Did your Mother have a particular team she liked?
Other Brother also supports Manchester United.
In fact, my German sister-in-law told me that the very first time they met (almost 30 years ago), at a time when he was already a comedy writer (and struggling actor - he performed at the Edinburgh fringe a few times, one year receiving excellent reviews from The Late Show, and the Guardian) - he had asked her whether she liked the Beatles and wondered which football team she supported. While she had no problem with the Beatles, she was a bit nonplussed to be asked about football.
My mother rather liked Ruud Gullit, - would murmur something about what an attractive man he was, (mind you, there was a time when she had liked Jermey Paxman as well, we used to tease her - she and I frequently used to watch Newsnight together) but no, she enjoyed the game - and was a sharp observer - but was not partisan in the sense that she supported no particular team.
However, she had been an excellent sportswoman in her youth, (and was an extremely good golfer in middle age) and would have made an exceptionally good analyst or commentator - she was an exceedingly keen observer of the game, and was entirely free of the emotional baggage that the rest of us had; she watched because she enjoyed it, and enjoyed teasing us.
For all of that, she preferred doing to watching. She had been Games Captain (hockey, tennis, table tennis, - as a young woman she was just under international level at the latter) and Deputy Head Girl at her posh boarding school, (A High Class Boarding Academy for Young Ladies according to its literature, which she used to quote, with a grin, years later), and - I think - would have loved (and excelled at) football if the opportunities that now exist for girls had been around in her time.
My father's fascination with cricket (which he indulged after he retired) and rugby, left her baffled. They both watched and enjoyed tennis, my father preferring the women's game, though my mother watched both - he disliked the brute power that had displaced elegance and class in the men's game.
Re support of teams: For my dad, I think that the Munich air disaster had an influence on him, for, even though he had liked United before that, I suspect that the Munich tragedy copper-fastened it- and Other Brother - following his father - strongly supported Manchester United.
In any case, I think that people come to support teams for a number of reasons: One - obviously - is geography, you support the local team; one is family identity - follow the team you dad supports, or be introduced to the traditions of a team supported by someone in your family; the third is the odd one out - when a team for some reason catches your eye and captures your heart; Decent Brother came to football as a small kid the year Sunderland won the FA Cup; for me, as a kid, it was probably the Arsenal Double two years earlier, and I knew as a child that I did not want to support Manchester United.