Why is English the official language of the European Union when Great Britain isn't even a member?

I’m wondering if the person who’s asking this question thinks that Great Britain and the United Kingdom are two separate countries. One used to be in the European Union and one has never been in. But it’s the same with air traffic. English rules the skies. It’s because of our empire. Britain were the original international traders since their explorers went everywhere, mainly because they were keen to get off the isle. Perhaps it’s the easiest language to learn rather than it’s done as a convenience. Our population may be greater than we realise since we have absorbed so many cultures. And once other countries began to trade with us, it would probably be easier to communicate with others rather than having to learn an entire third language. It is a bit weird since other countries would be bus disputing their borders whereas all the Brits had to do was to build a boat to tell them that they were there. It’s nice when things work out that way.