When you buy bitcoin on an exchange and leave it there, the exchange holds the keys. Your account shows a balance, but that is only a promise from the exchange to give you bitcoin when you ask.
When promises break
- Mt. Gox (2014): the largest exchange of its time collapsed, with around 850,000 bitcoin missing.
- FTX (2022): one of the biggest exchanges in the world went bankrupt after using customer funds. Withdrawals were frozen overnight.
In both cases, users who had withdrawn their bitcoin to their own wallets lost nothing.
Self custody
Holding your own keys is called self custody. It gives you what Bitcoin was made for: money nobody can freeze or lose on your behalf. In return, you are responsible for keeping your key safe, which is what the next chapter is about.