I can almost see the point.

(Disclaimer: this is purely speculative. I'd happily accept correction from TSOs who know the procedures ...)

I suspect that TSA's SOP says something simple like "have passengers remove sweatshirts and sweaters before screening". The reasoning, as has been pointed out, is that bulky versions of such apparel could be used to conceal "contraband" (however you choose to define it).

Now, what about tight sweaters, or shawls, or such like that? There are two alternatives.

• Allow the TSO to exercise their own judgment as to whether or not the sweater is "tight enough" to eliminate the possibility of smuggling. This is not without problems. Inevitably, different TSOs will use their judgment in different ways, leading to inconsistency in the screening process (which most of us complain about). Also, it could lead to certain embarrassing situations ... you can't necessarily tell if the bulge in a sweater is just a bulky sweater or just a really rotund passenger (like me).
• Have the TSO instruct passengers to remove all sweaters and sweatshirts, regardless of bulkiness or fit. This leads to absurdities like removing shawls. But it is easier to train on and standardize.

I suspect (but have no proof) that TSA has chosen the latter course as the simpler way to proceed.[/list]