This is an excerpt discussing Iranians and Kurds and I'm wondering if it is accurate as a rough summary.
"5 to 7 thousand years ago : Aryan people lived in the region of Siberia in today's Russia.
5 to 3 thousand years ago : Aryan tribes started to immigrate grudually , they split into 3 main branches, one immigrated to India, one to Iran, and 3rd branch went to Europe. Now it's important to understand this immigration didn't happen over night, and they didn't have their final destination already in mind! it happened during thousands of years.
3000 to 2500 years ago, different Aryan tribes settled in the plateau of Iran, they called it Iran meaning the land of Arya.
2600 years ago - first Iranian empire was founded by medians in west of Iran
With this view in mind everything starts to make sense, that Persians/kurds/afghans and many other people who live in Iran's plateau are rightly called Iranian people.
Their language and culture is also very similar and related. Who says Kurds have very different language from Persians? Their languages are so very close and of the same family. In fact if you wanted to choose a lanuage closest to kurdish it would definitely be Persian and vice versa. Same about culture.
Kurdistan is not considered occupied by Kurds who live in Iran. Ever since Cyrus the great established the persian empire persians and kurds lived together and been part of one entity. I mean suppose Medes were the ancestors of todays Kurds, Cyrus himself was half persian half median, his grandfather was the last king of Medians and he raised the persian empire by the help of medians. If you visit the site of perspolis you'll see carved on stone the pictures of Median and Persian soldiers standing next to each other.
So you see the name "iran" is not just about a political boundary which exists on today's maps. And the kurds don't feel they're occupied by this name! in fact they feel not only they're part of it but also they're one of the main founders of it."
Any thoughts on its accuracy?
This summary has a pretty large number of factual issues.
You are conflating a wider grouping of peoples, the Indo-Europeans, with the Indo-Iranians. In the past, both groups had been called "Aryans", but nowadays, that term has basically fallen out of favor. There are, linguistically, more than just three Indo-European groups. By my count, at least 10, with several more unrelated groups.
The standard model of how Indo-European speakers does seem to be that they started in the Pontic-Caspian steppe, which is in modern Ukraine and Russia, just north of the Black and Capsian Seas. This is not Siberia by most peoples' definitions. There are a variety of dates proposed, but yours are a bit older than most.
Defining something as a language or a dialect is often an inherently a political act. But linguistically, we can offer the criteria of mutual intelligibility. Meaning, can speakers of variety A understand speakers of variety B, and vice versa? Using this, it's obvious that at least Persian and Kurdish are not the same language. Persian speakers cannot understand Kurdish speakers, and it's almost certainly the case that not all Kurds speak the same language under these criteria.
You also have glossed over a large portion of Central Asian history and the history of the Iranian peoples (the linguistic grouping, which is much broader than peoples covered under the modern nation-state). For instance, you don't mention the Scythians or the Sogdians at all, both Iranian-speaking groups.