The facetious answer as to HMS Hermes's lack of inclusion is that the USN so dominates the public memory of the naval war that British and Commonwealth forces get pushed aside. There is some truth to this, but there are sound reasons not to stress that the Coral Sea battle was the first true carrier versus carrier battle.

For one thing, although Hermes had a large island and huge director platform, she was a very small carrier, even by the standards of the 1920s. Much like the American Langley and IJN Hosho, she was a first generation carrier and thus had a small air group. The 1942 Hermes only embarked a single squadron, 814 NAS, of Swordfish torpedo bombers. She maintained no fighter or dive-bombers as part of her air wing.

To make matters worse for Hermes during the Indian Ocean raid, the carrier had landed her Swordfishes when the Japanese entered the Ceylon area. Eastern Fleet commander Admiral Somerville had intended Hermes to be engaged in light escort duties off Ceylon in anticipation for her use in the invasion of Vichy-controlled Madagascar. But Nagumo's raid put Hermes in an awkward position in which she was in no condition to put up a credible defense, let alone attack the large IJN force. So Somerville ordered Hermes and an escorting destroyer, HMAS Vampire, to scatter from Ceylon and make for the relative safety of the Indian western coast. Unfortunately, this was too late for the British carrier and Shokaku and Zuikaku's dive-bombers found her.

The above brief sketch highlights a number of key differences between the Coral Sea and Indian Ocean battles with regards to carriers. In contrast to the Coral Sea's carrier battles, it was a completely one-sided affair. For all intents and purposes, Hermes was not a carrier in this battle but a highly-vulnerable and very visible ship. She literally had no aircraft on board and was completely dependent upon air cover from Ceylon. Even Shoho when facing Lexington and Yorktown's much larger air groups during the early stages of the Coral Sea battle could put up an anemic CAP in her defense.

Moreover, Hermes failed attempt at escape also demonstrates a different mentality than either side of the Coral Sea. Both Japanese and American commanders were aggressively seeking each other out once they became aware of the presence of enemy carriers in the area. Somerville, in contrast, was attempting to avoid a daylight battle with the Eastern Fleet in April and the Admiralty ordered the Eastern Fleet to make a strategic retreat to Kenya. Hermes being relatively old and of limited utility, found herself in a very vulnerable position of being an aircraft carrier without aircraft in waters where the enemy had air and naval superiority.

So while the proposition that the Indian Ocean raid was the first carrier vs carrier battle is technically correct, it really was not a carrier battle in the formal sense of the word.