Geologic pressure does come from gravity. For example the atmospheric pressure we observe comes from the weight of the air column above us. The matter at the center of the earth is surrounded by a uniform mass field and so the forces exerted on this matter are equal and opposite in all directions. It's really very simple. The thing that isn't so simple is that when we study gravitation we show that the gravitational field of any body acts as if all of it's mass were concentrated at its center of mass. And this may be true when that mass acts on something outside of itself, but it clearly is not true when considering gravitational forces within that body.
ML/NJ
So, if I could curl up and occupy that ONE point at the exact center of mass, all of the forces surrounding me would be equal and opposite in all directions. Fair enough. Off by a micron or two, though, and I’m smushed!