Why does Iran have a variety of ethnic groups?

Mehrdad, canım, I don’t know. I will guess, but whatever I guess, Dimitris Almyrantis will guess better.

Here goes.

• The usual answer is, Iran is at a crossroads of civilisations. Maybe. But you know, so is Greece, so is Turkey, so is Russia, so is Spain. In itself, that’s not actually an answer; it’s only the beginnings of an answer.
• Like many countries, Iran has ethnic spillover at its borders—Kurds next to Iraqi Kurdistan, Arabs in Khuzestan. That’s only a small part of it.
• Iran was in the pathway of a major population movement, that of the Turkic peoples. Unlike Turkey, that did not result in a demographic takeover: the Persian ethnicity was well-established and prestigious, and the Azeris and Turkmens were not waging a war of cultural or religous conquest when they arrived. But it did result in the Torki being a sizeable and secure minority.
• Iran was ruled by a multiethnic empire until fairly recently, which did not particularly care about how Farsi or Torki you were. (At least, that’s what you and Pegah tell me!)
• Multiethnic empires facilitated internal migration of different ethnic groups: hence the Georgians and Armenians in Fereydan (which is nowhere near the Caucasus), or the Circassians imported by the shahs.
• Iran did not have time or incentive to embrace the strongly centralising, “One Ethnicity One Nation” ideal that took hold of much of Europe. So there was not much opportunity for Persians to assimilate other ethnicities—even those closest to them, such as the Mazandaranis or Gilakis, let alone the Lurs.

So: some accidents of history, including the movement of the Turkic peoples; multi-ethnic empire; and lack of overt assimilatory policies. Shi’a religion and common cultural heritage, rather than ethnicity, have been entrusted with the role of binding Iran together.