If you want to ban saying something false then you need to start with arresting everyone who loudly and aggressively claimed that the murdered of the Democratic politicians in Minnesota was a far-left extremist and all of that. People are still claiming this, I believe.
Or maybe start with all the people who kept on claiming that migrants are eating people's cats and dogs.
etc. etc. etc. I can go on and on.
Applying the most strictest of strictest interpretation of the law for your enemies while being exceedingly lax with the law for your friends is one if the key hallmarks of authoritarianism.