Because the Turkic peoples are from the Altaic steppe, though that is not Mongolia it is a long way to the NE of Anatolia & the Turkic way of life was close to that of the Mongols. Modern Turks are probably not much to do with these peoples & likely have more ancestry in the pre-Turkic Anatolians.

I fail to see that this origin matters. Wherever your remote ancestors came from has little relevance today.

The Turks, or at least one ethno-cultural group of Turks, seem to have a shared history with the Mongolians.

Although I am not sure how much is political and how much is genetic. The Roman Empire went as far east as the Middle East and into the UK.

Think about the Mongol Horde and then look that up.