I understand fixies. I don't understand no brakes.

Why? Two reasons. First, I don't care if you're Eddy Merckx, Jan Ullrich, Lance Armstrong, etc., you cannot, and I repeat, cannot stop as fast by backpedaling as you can with good brakes. And I've had more than a few occasions where I've needed to make a quick stop. Secondly, redundancy. If your chain snaps, you have no brakes. I always want at least two ways to stop the bike, fixed or not.