There's also a setting that you can choose, so every window starts in private browsing mode by default. Go into tools, privacy, then in History, pull down to "use custom settings for history". You'll see a checkbox for "Automatically start Firefox in a private browsing session". Enable it, then restart firefox, and I think you'll have what you want. I'll stop bugging you after this post, it's certainly your prerogative to use whatever you want; it's just that you're hung up on something that doesn't seem either accurate or helpful to what you're trying to get at.
link with detailed steps of the process described in this post:
http://www.guidingtech.com/2046/priv...wsing-firefox/