Comment by 10000truths

Because the public key is the identity in the Wireguard protocol. If Alice and Bob want to communicate with each other over Wireguard, then Alice has to know Bob's public key, and Bob has to know Alice's public key. If they don't already know each other's public keys, then that information has to be exchanged in a secure manner at least once, in order to prevent nosy Mallory from impersonating one of them. How can Alice and Bob exchange their public keys securely? Not with Wireguard, because they'd need to already know each other's public keys for that! So they need to use some other secure mechanism as a bootstrap. Hence, out of band distribution.

In practice, Alice and Bob will often be two machines that are under control of the same entity, and that entity will transfer the key material from a third machine to the Alice and Bob machines over SSH or HTTPS. In those cases, the out of band mechanism is "SSH/HTTPS via trusted relay machine".