Don't be too impressed. I was wrong about what the double A icon does.
It removes text formatting. If you've made some text bold, changed the color, or some other thing, you can highlight it again and click on the double A icon to clear that formatting. It's a bit quicker than manually deleting the tags.
I thought it changed the editor because someone else noticed that if you couldn't edit in the box and clicked on it, then the problem went away. This still may be worth trying.
I'd have known better if I'd only spend a tiny amount of time checking my theory. All you have to do is hover the mouse over the icons to get a description of what each icon does.
You can still avoid the idiosyncrasies of the WYSIWIG editor by changing to the standard editor as a default, but it has to be done using Edit Options on the Use CP page. You almost have to do this for third party browsers, at least that is what it took to make Atomic play nice with the forum.