the simple or flavorful use of 'authority' usually just means someone is well respected on a topic "She's an authority on electrical motors" or that they posses some leadership qualities and are well liked.
the second and more dictionary definition of authority is authorization to rule. literally to dominate others because they are seen as legitimate.
your example of a club is a good test ground for these differences. it's up to you to run your club, make agreements with other members and share responsibilities even if people are happy to let you decide things or do most of the work. but your club doesn't have any claim to legitimacy, to true authority, because it doesn't seek to control ALL activities of that type. in the case of government, it very much does claim authority over the entire nation, to determine who can move where, who can work where and how, who must fight and who must be put to death.
there's no competition allowed with a structure like government. either obey or resist and face consequences. i'd much prefer a world of overlapping autonomous 'clubs' whose members decide for themselves than a world divided up by the greediest and most violent mafias.
It's very 'we have a plan' kind of thinking. The economic reality is far more complex and interwoven in real societies without government. I think people like david graeber are worth reading to kind of jump out of this intro-anarchist way of seeing the world.