I believe it might be better to stop defining Bitcoin as "money", and start thinking about it as a "ledger based on cryptographic proof, not based on trust"?
that definition doesn't make bitcoin not money. if people use it as money, then that's what it is. it's up to the market.
besides, i think it's important to convey that bitcoin isn't merely numbers on a screen. it's not created out of thin air. it has a distinct monetary policy, and is naturally a hard money because of its limited supply. the cryptography underlying bitcoin is not the whole story---the economic design is vital to making it work. the economic design is what makes it money.
bitcoin shouldn't be anything. it just is.