it means food that was produced in a factory
Factories can produce food I can make in my home.
I don’t understand why the location of the food matters.
You're stuck on the word "processed" as if it means anything that has been changed from its natural form, whereas it is meant to relay that a food has been industrially bulk processed and then packaged.
By your definition, cutting an apple is processing it, which is (hopefully) obvious that we're not talking about that.
The idea is to make your own food from as close to scratch as you can, to not eat pre-packaged "processed" foods like frozen pizzas and hot pockets and hamburger helper all the time.
Should we drink raw milk or should we drink pasteurized milk?