Why were they going to build The Bunker on Antikythera?

This is UFO related, but may seem off-topic. Antikythera is where the Antikythera Mechanism was discovered, which was featured on Ancient Aliens. Anyway, the titled question is a question I’d ask Lue Elizondo if I knew him, or others who have studied this event. I am just a humble scholar of history just hoping to learn more.

Before Greenbrier bunker was built, it was codenamed Project Greek Island. Before that, it was Project Casper. Before that, it was just Project X. While I’m not sure of the relevance of codename Casper, I learned it was renamed Project Greek Island because they planned to build the bunker on a Greek Island – Antikythera. For some reason the name stuck despite plans being finalized for the Greenbrier location. Why build a bunker completely outside of the USA – which doesn’t make sense from a strategic governmental continuity perspective.

I presume that X is of no significance, but speculate whether Casper refers to Wyoming. Or maybe it’s just Casper the friendly ghost. Or maybe Caspar the magi? But let’s get down to brass tacks – who builds an evil lair on an island other than Dr. Evil? Honestly?