The first step in building a holographic duality from first principles is the identification of symmetries. Operators in a CFT are naturally arranged into conformal families. I will demonstrate that the conditions defining a CFT conformal family are equivalent to the Fierz-Pauli system of equations in AdS, with a mass set by the dimension and spin of the associated primary operator. This illustrates how linear Einstein gravity in AdS arises seamlessly from basic statements about the CFT stress tensor. Analogous constructions are given for dS and flat space.