general relativity - Why do objects follow geodesics in spacetime?

Trying to teach myself general relativity. I sort of understand the derivation of the geodesic equation

$$\frac{d^{2}x^{\alpha}}{d\tau^{2}}+\Gamma_{\gamma\beta}^{\alpha}\frac{dx^{\beta}}{d\tau}\frac{dx^{\gamma}}{d\tau}=0.$$ which describes "how" objects move through spacetime. But I've no idea "why" they move along geodesics.

Is this similar to asking why Newton's first law works? I seem to remember reading Richard Feynman saying no one knows why this is, so maybe that's the answer to my geodesic question?