Fix: error: failed to push some refs to …

This is a summary line. The real reason is in the lines just above it, so read the whole output. The most common version looks like this:

 ! [rejected]        main -> main (fetch first)
error: failed to push some refs to 'github.com:owner/repo.git'
hint: Updates were rejected because the remote contains work that you do not
hint: have locally.

You will also see (non-fast-forward) instead of (fetch first) when Git already knows about the remote commits. Both mean the same thing: the remote branch moved on since your last pull, and pushing now would throw those commits away, so Git refuses.

Fix: integrate, then push

git pull --rebase
git push

--rebase replays your local commits on top of what is on the remote, which keeps history straight. If you prefer a merge commit, use git pull --no-rebase. If you run plain git pull and get Need to specify how to reconcile divergent branches, pick one of these flags, or set a default once with git config --global pull.rebase false (merge) or true (rebase).

If the pull stops with a conflict, fix the marked files, git add them, and run git rebase --continue (or git commit after a merge). Then push.

You rewrote your own branch on purpose

After git commit --amend, git rebase, or git reset on a commit you had already pushed, the remote has the old version and rejects the new one. Pulling here would bring the old commits back. If the branch is yours alone, overwrite it safely:

git push --force-with-lease

This only succeeds if the remote still points where you last fetched it; if someone pushed in the meantime you get stale info instead of silently deleting their work. Avoid plain --force, and never force-push a shared branch such as main.

Other causes with the same last line

• error: src refspec main does not match any: there is no local branch with that name. Either you have not made a commit yet, or your branch is called something else. Check with git branch, and push the name it shows.
• A line starting with remote: that mentions a protected branch or a rule: the repository does not allow direct pushes to that branch. Push to a new branch and open a pull request.
• remote: lines about authentication or permission: your credentials are wrong or you lack write access. See the git remote -v URL and your SSH key or token.
• pre-receive hook declined or a message about file size: the server rejected the content itself. The text after remote: says why.

Avoid it next time

Run git pull before you start work and again before you push, and keep your work on a branch of its own rather than on a shared main.