I am wrong?
First. I did not say that the FIRST US jet took of from Essex class, I did say that US Navy deploy jet aircraft in Essex class aircraft carrier.

I also think I may have misunderstood your sentence. I assumed that you meant US Navy had to wait until the deployment of Midway class carrier to be able to operate jet fighters on carrier.
But if what you actually meant that the first US Navy jet aircraft was taking off from Midway class carrier then you are right.
Second; You are saying that Zepp was to small to have jet fighter, I did not agree wiht that. The difference of Essex' and Zepp's length was more or less 10 metres; therefore I believe they can carry those jet. And the fact that first operational jet squadron was on the USS Saipan( length of 684 feet), a CVL which I think much smaller than Essex(872 feet), support my point even more.

And the Zeep was (262 metres or 864 feet)
If you are refering about the picture read the caption carefully, "......was the first carrier to launch banshee twinjet fighters on combat mission." It didn't say that Banshee twinjet fighters was the first US jet in the carrier. And I agree with you that FH-1 Phantom was the first Navy's jet to take of from carrier.