Earlier quoted context omitted.
One of the biggest differences is that if you're using password auth, and you are tricked into connecting to a malicious server, that server now has your plaintext password and can impersonate you to other servers. If you use a different strong random password for every single server, this attack isn't a problem, but that adds a lot of management hassle compared to using a single private key. (It's also made more dif…
Not a rhetorical question: couldn't the malicious server relay the challenge from a valid server for to you to sign, and impersonate you that way?
If I am a server and have your public key in an authorized_keys file, I can just encrypt a random session key using that and only you will be able to decrypt it to finish setting up the session.
This is why passwords and asymmetric crypto are worlds apart in security guarantees.