TLDR Version:
A private key is the literal key to accessing your private wallet. It is so secure that not even the CIA can hack it! (Or can they?)
Custodial wallets such as Coinbase hold the private keys for you.
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Not until what's known as the doomsday scenario arrives, when an algorithm for predicting prime numbers efficiently is derived. Hence all the talk about governments wanting to introduce backdoors.
Yes holding your private keys is critical and as you say custodial wallets fail in this respect. More to come in part 2! Thanks for the concise TLDR 😉