Why Nostr uses public/private key cryptography ?

Your identity on Nostr is your key pair. There's no username/password database, no company that owns your account. Your private key signs every event you publish, proving you authored it , without trusting any third party. Anyone can verify your signature using your public key. This means your identity is self-sovereign: no platform can ban "your account" because your account is just a math relationship between two keys that only you control.