GitHub authentication failing over https, returning wrong email address

Initiating a push or any other action with GitHub from the command line (over https, not ssh) that calls for the username and password not only fails but, when it does, it returns

Username for 'https://github.com': username
Password for 'https://[email protected]': 
remote: Invalid username or password.
fatal: Authentication failed for 'https://github.com/username/repository.git/'

I do not have an @github.com address. The password and username are correct.

I know I could switch to SSH and use keys but that doesn't answer why the authentication is failing over https.

GitHub's support determined the root of the issue right away: Two-factor authorization.

To use GitHub over the shell with https, create an OAuth token. As the page notes, I did have to remove my username and password credentials from Keychain but with osx-keychain in place, the token is stored as the password and things work exactly as they would over https without two-factor authorization in place.

I do not have an @github.com address

You don't have to: the @ is the separator between the username:password and the domain.
It is not an email address.

A full GitHub https url would be:

https://username:[email protected]/username/reponame.git

Without the password (which would then be asked on the command line), that would gave:

https://[email protected]/username/reponame.git

But again, [email protected] isn't an email address, just the first part of the credentials.

Make sure the case of your username and reponame is correct: it is case sensitive.

Note that you can store and encrypt your credentials in a .netrc.gpg (or _netrc.gpg on Windows) if you don't want to put said credentials in clear in the url.
See "Is there a way to skip password typing when using https://github".