This phrase always struck me as odd. It means hoping for something when reason tells you there’s no way it’s going to happen. So it’s really hoping against all reason. Hoping against all hope would be like… I don’t know… hoping for something to happen that everyone else is hoping won’t happen, or maybe hoping simultaneously for something to happen and not to happen. I thought maybe that this was an example of a phrase that originally had a logical meaning but was mangled over time like “The proof is in the pudding”, but evidently it comes to us straight from the Bible.
That’s all… mundane and pointless for sure. I can’t think of any other common phrases like this (except the mangled ones like “the proof is in the pudding”).