By default, the ssh client will try all keys it found in the ~/.ssh directory.
So if you have a lot of them, it can be problematic because it will failed a lot of time and eventually be kicked by the SSH server with this error:
Too Many Authentication Failures
To avoid this behaviour, add the following option to the command line (or directly in the ssh configuration file)
IdentitiesOnly=yes
And then specify the method you want to use
ssh -o IdentitiesOnly=yes -o PreferredAuthentication=pubkey -i ~/.ssh/my_new_key root@<ip>