After this lesson you can: answer "why is it worth anything?" without hand-waving.
"What backs it?" is the first question, and the honest answer is: nothing, in the sense of a promise to exchange it for something else. The same is true of the dollar since 1971. Value does not come from backing. It comes from usefulness and scarcity.
Useful as money
Go back to the tests from Money 101. Bitcoin is scarce (21 million, verifiable), durable (the ledger is copied on thousands of machines), divisible (100 million sats per coin), portable (a seed phrase crosses any border), verifiable (run a node) and fungible at the protocol level. It can be sent to anyone, at any time, and no one can stop a valid transaction.
Scarce, absolutely
Gold is scarce because mining is hard, but more is found every year and no one knows the total. Bitcoin's supply is fixed by rules every node enforces. Higher prices create more gold mining; they cannot create more bitcoin. That is new.
Then why the volatility?
Because it is young and small compared with the money it competes with. A money being adopted from zero cannot have a stable price along the way. The question is whether its properties are good enough that adoption continues. So far, every cycle has ended with more users, more infrastructure and a higher floor.
Gold has about 1.5–2% new supply a year. Bitcoin's new supply is now under 1% a year. Which is scarcer by issuance: (1) gold, (2) bitcoin? Enter the number.