"When a club discusses who should or should not remain members it is all the existing members who have a say, not just the member concerned. "
But this isn't the same as a club deciding who should be its members. It's a voluntary (these days) union of 4 nations. Scotland being kept in the UK, or removed from it, against its own wishes, by the votes of people elsewhere in that union, would be wholly unacceptable.
On the other hand suppose The Republic of Ireland wanted to join, or Scotland did something nasty that made its expulsion a possibility, then a UK-wide referendum might make more sense.