If you have your private key(s) in ~/.ssh and have added them to https://github.com/settings/ssh, but still are unable to commit to a Github repo added via ssh, make sure they are added to your ssh-agent:
ssh-add -k ~/.ssh/[PRIVATE_KEY]
You can add multiple private keys for multiple servers (e.g. Bitbucket & GitHub) and it will use the correct one when dealing with git.