Mosaddegh was appointed by the Shah. He wasn’t elected by the people. He then started a bunch of shenanigans against the Shah but didn’t have the support of the mainstream so he was forced into alliances with the radicals — the Islamics and the communists. The US didn’t like that because it posed a risk of Iran and its energy resources falling into the Soviet orbit. Remember, this was the height of the Cold War. The whole Iran thing was really a proxy struggle between the US and the Soviet Union. The Soviets had their agents in Iran assisting the anti-Shah forces all the way up to the revolution in 1979 and beyond. The current alignment between Iran and Russia goes back to the Cold War era.
Mosaddegh was Iran’s constitutionally appointed prime minister with parliamentary backing. The Shah formally ratified the position but he was duly elected, largely on the platform to nationalize the Anglo-Iranian Oil Company. He ran a basic MIGA platform- Make Iran Great Again. Britain was having none of that and pressed MI6 into service to repackage the threat to the BP corporation ,
by calling Mosaddegh a communist, knowing that the CIA would take the bait which they did. Flash forward decades and watch us fall for the same scam.l only this time it’s Israel repackaging Iran as “WeEks awAY FrOm sETting OfF a NUKe oVer Washington and New York!!” History repeats-first as tragedy, then as farce.