AWA adding to Miguel’s post.
I was planning on doing an entire post regarding this.
The short version is that in 1934 Congress knew that the right to keep and bear arms could not be infringed. The only constitutional power they had was to tax. Thus the NFA is a revenue generating bill. It describes what should be taxed.
The intent was to make the weapons of crime to expensive to own. The targets were machine guns, sawed off shotguns, silencers, and pistols. Yep, pistols.
Considering that a Thompson machine gun between $170 and $200 in 1930 and that was considered a very expensive machine gun, a tax of $200 would double the cost of the Thompson.
A Colt 1911 would cost you around $22. So a nearly 10x tax on a top of the line pistol.
Somebody figured out that if they made pistols “taxable” under the NFA that people would just cut down rifles which were not going to be taxed. So instead of having a nice pocket pistol, you would have a cut down rifle in your pocket. So they added the concept of a short barreled rifle to the NFA.
The legislature got some feedback saying “don’t you dare ban/tax our pistols!” so removed pistols from the NFA. Nobody was concerned about the short barreled rifle clause so it was just left in.
Ian, in the linked video, talks about how the definition of a short barreled rifle changed over time. It is an interesting listen.