Fungibility means each unit is interchangeable with any other. One banknote is as good as another, regardless of its past.
The problem
Bitcoin's history is public. In principle, someone could treat coins differently based on where they have been: an exchange may ask questions about or refuse coins with certain histories. If coins with a "bad" past become worth less, every recipient has to check the history before accepting payment. That is costly and makes money worse at its main job.
Why privacy and fungibility are linked
The less a coin's history reveals, the less basis there is for discriminating between coins. Privacy for individuals therefore protects the money itself, not just secrets. This is the same reason cash is valued: the shop does not need to know where your note came from.
Bitcoin's answer
- At protocol level, every satoshi is valid. The network does not care about history; rules apply equally to all coins.
- Good habits reduce linkability: fresh addresses (no address reuse), coin control and running your own full node.
- Tools such as coinjoin and payjoin make the common analysis assumptions less reliable.
Honest limit: in regulated businesses, the history of coins can still be checked, and that will remain. Fungibility in Bitcoin is strong at the protocol level and depends on user habits at the surface.