"I sit on the pillow."
Translation:אני יושב על הכרית.
Well... because it isn't. A pillow can be a direct object in a sentence, but "sit" is an intransitive verb, which means there can't be a direct object after it, only an indirect object. And an indirect object can take any other preposition, like על here, or can be without a preposition.
You can never say את על because את is always used with a direct object and על is always used with an indirect object. An object cannot be both direct and indirect at the same time!
Now אני יושב את הכרית would mean "I sit the pillow" which doesn't make much sense. There are very few direct objects you can sit without any preposition, and "pillow" is not one of them.