What is the "login with NFT" option?

Wouldn’t it still point to the owner address? Can you please explain how this is a different identity

Login with NFT will provide different identity than owner address. This identity will have it’s own email address and (probably) dedicated mailbox.
After transferring NFT, the new owner will be able to use it to login to various services and will effectively take over this identity.

I don’t have the details nailed down yet so this is only a initial thought.