I've got a wild theory, so hear me out. Maybe Britain wanted to be governed by a set of law's made by British people?
EDIT:
I can't reply to the comment below for some reason, so here's what I was going to say:
Much of the EU's unpopularity amongst the Brexit-supporting section of the UK's population comes from it repeatedly being used as a convenient scapegoat for domestic political issues, and the country's most-read newspapers printing decades of nonsense ("EU bans yogurt and cheese from school dinners", "EU bans straight and bendy bananas", etc.) that were taken as fact about what a broken institution it is.
Brexit was really just the end result of a spectacularly successful sustained propaganda campaign.