> What makes this browser plugin illegal software that is worthy of a ban?

It isn't illegal. Facebook isn't a legislative body or a court, it can neither create nor adjudicate law.

And you can read Facebook's case via their cease and desist letter linked in the article.

> What else can Facebook demand that its users use or don't use?

Outside of their platform? Nothing, obviously. They're not going to break into your house and burn your books or anything.

Exactly, Facebook cannot dictate what software one can make or run. They can claim a terms of service issue and ban you from their service but they cannot stop you from developing software.

If it were me, I'd be tempted to martyr myself just to show how fucked up Facebook really is. What is the worst that can happen? The guy goes bankrupt. Life goes on.

The issue was 'automating user interactions'. The demand is 'I agree to never again create tools that interact with Facebook or its other services'.

That demand is wrong. What if the developer makes an extension for some other web site and then FB buys that site? They'll go the legal route again. I don't think that is right.