Why did wounded soldiers never bite the bullet?

Soldiers NEVER "bit the bullet" because even though there were .75 caliber (3/4") bore muskets during the Revolutionary War and .72 caliber rifled muskets in the American Civil War those bullets are STILL small enough to slip from between the teeth and into the throat, choking and killing a wounded soldier. Add in that lead is not soft enough to keep from breaking teeth and you have the two primary reasons no one "bit the bullet."

During the American Civil War whenever ether or opium were not available (used in most surgical procedures) surgeons would provide a thick, wide strap of green (uncured) leather big enough in width and length that could not possibly be taken fully into the mouth, much less swallowed to obstruct breathing. Additionally, the green leather was soft and resilient enough that it would absorb the bite force without cracking or breaking teeth.

ALL of the bullets sold as so called "pain bullets" from the Civil War are actually bullets that have been rooted and chewed by pigs over 150+ years. Pigs' molars are virtually identical to those of humans (four points) and the chewing resembles that which might be done by humans, but was not.

Don't buy a pig bullet misrepresented as a "pain bullet."

Not sure of your question; but the saying came about as in field surgery they would bite a lead bullet to prevent bitting tongue as pain meds where few if any in say the civil war time.