Iranians feel most offended when they are treated as Arabs.
Iran is in the Middle East like the Arabs, has similar characters in writing, and above all, it's easy for us to think that Iran is also Arab because they share the same religion, Islam.
However, Iran is not Arab. Iran is Iran, and Arab is Arab.
Iran and the Arabs are very different in many ways. They are different in ethnicity, language, and even religion.
Moreover, the relationship between Iran and the Arabs has not been very good for a very long time. The relationship between Iran and the Arabs is similar to that of historical enemies. It’s understandable that they would be upset if referred to as Arabs, given that their relationship is not good to that extent.
This video discusses the differences between Iran and the Arabs and why they are like enemies.