As I understand it, an SSL certificate is supposed to authenticate a host as it's signed by a third-party organisation.
If a MitM were to intercept this showing of this public certificate to the client, couldn't they just make a copy of that signed certificate, and then claim to be the host? I understand that the MitM wouldn't have the private key, but it seems as though they can still pretend to be the authenticated host and just not be able to decrypt data that has been encrypted by the public key.