A-to-Z Challenge! Open! Because!
Open comes from the Old English open, which meant…not closed. Okay, they’re not even trying. Anyway, it comes from the Proto Germanic upana, put or set up, and Proto Indo European upo, over or up from under. If you think that word looks like up, it’s because it’s the origin of up, as well as the prefix sub-, which is used to indicate under.
So it goes from over to set up to not closed. Man, etymology is usually vague, but even I can’t see the thought process behind this one.
Tony Jebson’s page on the Origins of Old English