What law specifically denies unemployment benefits to a sole proprietor?

I understand that the employer can not pay himself a salary, pay payroll tax on his salary, and then collect payments if he goes out of business. I would like to know specifically where this is addressed in federal law or D.C. law.

It is not Federal, but State Law. In your case DC Law.

1.) Since you are a business you have control.
- YOU CANNOT FIRE YOURSELF

2.) Also the big one - YOU ARE NOT PAYING UNEMPLOYMENT TAXES
- SO WHY would you expect to receive distributions.

Are you serious?

Laws define legal obligations & restrictions rather than making every act that constitutes a "lack of common sense" either legal or illegal. The law doesn't specifically say you cannot make yourself the sole beneficiary of your Will, either, because it assumes you have enough sense not to do that!

If you are a sole proprietor, you are the only person who is in a position to decide if you should stay in business or not. I should not have my taxes pay your wages because you decided to go home!

There doesn't have to be a law denying it - if there is no law permitting it, it isn't available.

It's logical if you think about it - otherwise would be too open to abuse by someone who worked just long enough to collect, then collected for half a year, etc etc etc