In a 1967 paper [1], G. Feinberg conjectured about the possibility of “faster-than-light” particles. In the current note we prove his conjecture to be false by showing that he missed several key counter-arguments to their existence. We explain why the existence of tachyons contradicts both relativistic kinematics and relativistic dynamics. Our paper is divided in two sections: the kinematic counter-arguments and the dynamics counter-arguments.