general relativity - Intuition for why mass and energy curve the space-time fabric and for why this relationship is linear?

The force of gravity does not exist

I understand(-ish) that, following general relativity, an apple falls onto earth, not because there is a force pulling earth and the apple toward each other but because, both the earth and the apple are travelling through time in the same direction and that their mass curve the space-time fabric causing the geodesic of the movement through time to "fall" down the same location in space.

Why does mass and energy curve space-time?

I don't understand why mass (and energy) curve space-time. I am "familiar" (I never saw any explanation about it) with Einstein equation putting $T_{\mu\nu}$ (Mass and energy) and $G_{\mu\nu}$ (space-time geometry) in a linear relationship but I fail to get an intuitive explanation for why such relationship between $T_{\mu\nu}$ and $G_{\mu\nu}$ exist and why it has to be linear. Note that I don't really understand the true meaning of $T_{\mu\nu}$ and $G_{\mu\nu}$ but only the vague description that I made of them.

Question

In short, my question is

Can you give me an intuition for why mass and energy curve the space-time fabric and for why this relationship is linear?