A lot of developers wound up using Firefox to develop web apps even when the web app was intended to be used in IE. That's important because it broke the vicious cycle where nobody used Firefox because nobody developed for Firefox and nobody developed for Firefox because nobody used it.
You might use other extensions, as do I, but this is such a deal-breaker that barely anything else matters. The browser that runs your dev tools will be able to run your app, obviously, so being the browser with the good dev tools is a tactic to make sure web pages will actually run in it.
The constant rhetoric around extensions is an irrelevant sideshow. It's the web pages that actually matter. Nobody would have bothered to use Firefox unless the majority of web pages they use work in it, and Firebug is the primary reason why so many web pages did work in it, along with Google strategically choosing to support Firefox as a way to hedge their bets against Microsoft making adversarial changes to IE to cut Google off.