To be fully honest I don't think anyone really knows for sure, this particular event is extremely complicated with many factors involved. This is my take it on it.

I would like to argue that one of the biggest reasons was his strong policy for modernization and secularization. This made many Islamists angry. Iran was developing rapidly and there was a portion of the population who didn't enjoy that. Back when the Shah gave women the right to vote and encouraged them to participate more in society, Khomeini and his followers strongly opposed this. Protests did follow after this in the 1960s. Many of the beginning demonstrations and protests were done by these people. It is worth noting that considering that some portray the Shah as brutal, he did let these demonstrations and protests take place against him and his government.

During the Cold War Iran also had multiple terrorist groups who were extremely active and supported by different states. We had multiple communist organizations whose goal was to overthrow the Shahs government and replace it with a pro-Soviet Union communist organizations. Basically the revolution begun by an alliance between the Islamist and the communists. Why did these groups exist? Well, because they felt that it would be better for Iran if it had a communist government. These types of organizations existed in most nations, like the Red Army Faction in West Germany.

This is in my opinion the most important reasons. There were other things that played a role, one example was when Irans economy took a major hit in the late 1970s with rapidly increasing inflation and a massive decrease in oil income because of a US-Saudi plot against the Shah which caused discontent among a population that was to a economical boom. There was also corruption among the government, like any other nation, and the Shahs relatives. I don't personally think the Shah himself was corrupt. There were also certain events that fueled the protests and triggered the revolution, one example is Cinema Rex fire where everyone at that time blamed the Shah and SAVAK, later it was disclosed that neither the Shah nor SAVAK was responsible for it but the Islamists who put the blame on them.

Obiviously this is extremely simplified. There is so much more. Many Iranians today also believe that the US and UK helped overthrowing the Shah, evidence to support this exists. Basically in my opinion the protests were like any other protest in any other nation. Something interesting is that there was a significant amount of protesters who were armed during the revolution, where were they getting the weapons from?