This is one of those common-sense features which users take for granted in other programs, but which AI sorely needs to update.
AI has reverse-direction buttons in the Attribute Palette, but they only work on sub-paths of compound paths. Other programs let you reverse the direction of any path. AI should have added this long ago.
The workaround is, you have to take advantage of the (in my opinion ill-conceived) auto-merge behavior of the pen. When you click the end of an open path with the pen, (even an UNselected path--insert RAGE here), it "helps" you by assuming you want to add another segment to the path. So it makes the endpoint under your cursor become the last endpoint when you click. Of course, you have a 50/50 chance of guessing whether this endpoint is *already* the last point of a path, so you often have to undo, and then click the other end if nothing happens on the first click. Yes, I think it's stupid to have to invoke the Pen tool in order to simply change the direction of a path, but that is the workaround you will invariably receive as the "norm" here.
On brushes which I use frequently, I usually just find it easier to make a duplicate brush with the artwork reversed. That way, I can just click the one I want to apply to a selected path, and if the results goes the wrong way, my cursor is already in the right place to just click the other brush in the palette.
Again, this is typical of the kind of inefficiencies which saturate AI, and which I want to see cleaned up far more than I want new whizbang features. (Another one related to this topic is the failure of the Brush tool to respect the stroke weight set in the Stroke Palette.)