The reasons are this: anyone can use the tools without have to learn anything, it's really quick, the way it works tends to make you keep things simple (very important), you can create a template page and then cmd+V it across all the other pages (slides), you can scroll through the pages (try doing that in Photoshop), easy output to pdf/jpgs etc if you want to share and of course if you want to present the design...well 'nuff said.
If you're designing for Twitter I'm assuming that graphically you're doing something very clean and simple. This method helps you keep it that way.
I usually stick to a fat pen and paper or whiteboard. When I'm done, I scan each page or take photos of sections of the whiteboard and then load them up as a presentation in Google Docs (easy to share with partners).
No losing papers or accidental erasures there!
"I have this twitter-based idea. I've brought a pencil so you can stab your eyes out while I explain"
It will also help later on in allocating tasks and workflow to other members of the team. As you develop code just update the prototype.