I disagree that the choice is “arbitrary”.
If you accept that a sports team is representative of a particular group of people - usually a city, but also nation - and you belong to that group of people, it makes sense to identify with a particular team.
So… my mother is from Liverpool, therefore I have an attachment to Liverpool. It’s also natural to associate with success, and when I was a lad Liverpool were the dominant team in the UK.
You might support a team who’s playing style and management philosophy most closely mirror your own world view - the rough ‘n’ tough Glasgow Rangers, or the cultured play of Arsenal.
You might choose a team because your brother supports their greatest rival - Everton vs Liverpool, Spurs vs Arsenal etc
It might be that by chance you attended your first game at a particular club, which will give you a greater affection for that team. Or maybe the supporters at a club were particularly welcoming, and made you feel part of a group.
Seriously, there’s millions of good, rational reasons why an individual might choose to support any given sports team…