Learn Turkish: Bunun yerine, asıl yanlış olan unsuru gözden kaçırıyorlar. - Instead of this, they overlook the truly wrong element.

By combining asıl (the actual/main) with the relative participle olan (which is), Turkish singles out this specific element from other possibilities. It feels much like saying "the element that is actually the wrong one" rather than just "the wrong element", placing heavy focus on its wrongness.

Could we just say asıl yanlış unsuru without olan?

Yes, you could just drop olan to mean "the actual wrong element". However, adding olan is exactly what creates the emphasis your lesson covers. It stretches the phrase out to mean "the element that is the wrong one", shifting the spotlight directly onto the adjective yanlış.

What is the literal translation of the idiom gözden kaçırıyorlar?

It literally translates to "they let it escape from the eye". The verb kaçırmak means "to let escape" or "to miss" (like missing a bus), and gözden is "from the eye" (using the ablative case). Together, gözden kaçırmak is the standard way to say "to overlook" or "to fail to notice".

Why does unsur take the accusative -u suffix here?

The noun unsur (element) is the direct object of the verb gözden kaçırıyorlar. Because it is specifically defined by the modifying phrase asıl yanlış olan (the one that is actually wrong), it is a specific direct object and therefore requires the definite accusative marker.