Why must I force push after changing a commit message?

By amending commits, you are changing their SHA1, which means the local and remote history are no longer the same.

If you want to replace the remote history by your (amended) local one, you will need to force push.
If you don't, Git will refuse the push, and ask you to pull (which in this case is not helpful, as you would merge with identical content but different commit messages)

Force pushing can be dangerous as it forces other collaborators to reset their own local history to the new (forced pushed) one.

As commented, --force-with-lease is safer (if the remote branch you are changing was itself changed since your last pull, meaning other were actively using it and pushing it back, then the forced push is denied).
Combine that with a sensible pull policy (where you always rebase what you have not yet pushed), and force pushing becomes less needed.