Short answer: because of Islam ([Shia](https://en.wikipedia.org/wiki/Shia_Islam), specifically).

More detail: most people were uneducated and mostly Muslim, so [Khomeini](https://en.wikipedia.org/wiki/Ruhollah_Khomeini) used this to provoke people against [Mohammad Reza Pahlavi (king of Iran)](https://en.wikipedia.org/wiki/Mohammad_Reza_Pahlavi).

A few years before Khomeini came to power, Mohammad Reza Pahlavi implemented the [White Revolution](https://en.wikipedia.org/wiki/White_Revolution) to modernize Iran (including granting women the vote, land reform, etc.). Khomeini opposed these reforms and considered them contrary to Islam. Eventually, with support from some [communist parties](https://en.wikipedia.org/wiki/Tudeh_Party_of_Iran) and promises of free buses, electricity, and similar benefits to peoples (like what Zohran Mamdani did), the king was overthrown and Khomeini took control.

Interestingly, Khomeini subsequently suppressed and eliminated the communist parties, seized factories and homes of those who opposed the Islamic Republic, and labeled many opponents as terrorists and enemies of Islam.

To understand what Khomeini and the Islamic Republic enacted: - Chess was banned for a period as being against Islam. - Sexual relations with children were publicly condoned by Khomeini in his writings. - ...