First, let me be more specific in my original reply:
A footnotes summary is that having been rebuffed in his attempts to sell a 308 AR, Stoner quickly modified the 222 Remington cartridge and made a smaller rifle to sell to the Air Force as a replacement for the M1 Carbine.
His choice of bullet was limited to what was available and easily modified.
Not correct. In
April 1952, Aberdeen grants the request of Gerald Gustafon (who along with William C. Davis did the 60gr .220 Swift study for Aberdeen) to study
Small
Caliber
High
Velocity cartridges for use in rifles and carbines.
In Novemeber 1952, Gustafson modifies an M2 Carbine to fire a .224 bullet based on the .222 Remington case shortened to 1.32" (.22 SCHV) firing a 41gr round at 3,000fps. In September 1953, he publishes the results of his findings which conclude that the .22 SCHV is superior to .30 Carbine and .45ACP and compares favorably with the .30-06 M1 out to 300m. He recommends further testing to the Infantry Board. By the time the report is issued, Project SALVO is already well underway and evaluating calibers from .18-27 in both simplex and duplex rounds.
April 1954: Davis and Gustafson submit a new report on the advanatages of SCHV cartridges. They propose a .22 cartridge based on a .224 caliber 68gr bullet in a necked down ".30 Light Rifle" (what would eventually become 7.62x51mm) case fired at 3,400fps. This report gets them approval for further research on this cartridge which is dubbed ".22 NATO"
In December 1955, just as Springfield Armory is nearing completion of the .22 NATO T48 (FAL) conversions, Davis and Gustafson publish more findings on .22 NATO and request additional funds. These funds are denied. A key feature of this latest report is the proposal of a new SCHV cartridge in between .22 SCHV and .22 NATO - this new cartridge would launch a 55gr bullet at 3,300fps (sound familiar?)
December 1956 - a copy of the "denied" funding request by Gustafson and Davis makes it to the desk of General Willard G. Wyman, Commanding General of the Continental Army Commnd. Wyman recommends that the Infantry Board submit a formal request for a SCHV rifle based on the cartridge in the denied funding request. Wyman also hints to Eugene Stoner that a scaled-down version of his AR10 rifle prototype might be a good match for the Infantry Board request.
Spring 1957 - The infantry board extends the original 300yd range to 500yd in order to address dissent amongst Army officials. As a result, all the various manufacturers are forced to revamp their .22 centerfire ammo designs to meet the new requirements. Stoner tweaks the .222 Remington round to meet the new requirements - more case capacity is needed to meet the velocity (3,300fps as it turns out) necessary for 500yds - leading to the ".222 Special"
May 1957 - Stoner demos a prototype of the AR15 for General Wyman. CONARC formally requests 10 AR15s for testing in .222 special (5 days after the adoption of the M14 is announced).
November-December - several SCHV rifle submissions are demonstrated by Winchester and Armalite. However, the revamped Winchester .22 still doesn't meet the penetration requirements. Winchester redesigns the case but retains the short OAL so that they don't have to redesign their rifle entry. The Armalite can fire either the .222 Special or the .224E2 Winchester - so the trials go forward with the .224E2 Winchester.
In July 1958 the Infantry Board releases a study concluding the AR15 and Winchester SCHV entries are a potential replacement for the M14, In September of the same year, CONARC judges both rifles superior to the M14. The AR15 is judged superior to both M14 and Winchester in terms of reliability, however the .222 Special and .224E2 Win cartridges are judged inferior to 7.62x51. In December of this year, artic testing of the SCHV rifles takes place.
1959 - .222 Special (Stoner's design) is renamed .223 Remington. The Powell Board approves of the SCHV concept and recommends the purchase of 750 AR-15s for extended trials; but recommends no further consideration be given to .223 Remington. In January, Colt enters into a licensing agreement for the AR10/AR15 with Fairchild/Armalite.
July 1960 - the infamous Curtis LeMay party with the watermelon.
Now keep in mind, this lengthy post is a very brief summary. I've eliminated hundreds of studies on .22 rifles and projectiles from this time period just to hit the points that are directly relevant.
1. Stoner did not make the rifle to sell to the Air Force to replace the M1 Carbine. Stoner scaled down the AR10 at the request of General Wyman for the SCHV rifle program.
2. Stoner didn't just pull the .222 Remington out of his rear. He used that caliber because the SCHV program specifically asked that he used something very similar to .222 Remington and it asked that because of much previous research on the subject.
Again, look at the very helpful
Gun Zone 5.56x45 timeline. It goes into excruciating detail on the subject. There is a decade of research on .22 centerfires prior to the LeMay party and at that point, the AR15 was already being evaulated by the Continental Army Command as a serious replacement for the M14. LeMay was certainly instrumental in making the AR15 happen; but I think your short summary is so concise that is misstated the historical facts as well and not being very clear on why .223 Remington was ultimately chosen.