>that mitochondrial DNA is printed from some subset of the 46 chromosomes

It's not.

Don't think of mitochondria as just another organelle. Think of them as something similar to a parasite that lives inside your cells, except it's beneficial.

They have their own DNA, they reproduce independently. They aren't formed in the zygote, they already come inside the egg. They spread from mother to child this way for billions of years. Each time a cell divides, some of them go along.