Make sure your GitHub ssh authentication isn't set up right, i.e.., you don't have your public keys set up, i.e., the ssh -T test fails.
Clone a public repo from GitHub.
Make some changes, commit, and push. Even if you have push access on GitHub, this will fail because of the bad ssh authentication, but Elegit's error messages don't help you figure that out.
Here's the specific scenario (thanks to @mgorra):
Make sure your GitHub ssh authentication isn't set up right, i.e.., you don't have your public keys set up, i.e., the ssh -T test fails.
Clone a public repo from GitHub.
Make some changes, commit, and push. Even if you have push access on GitHub, this will fail because of the bad ssh authentication, but Elegit's error messages don't help you figure that out.