One of the postulates of the (special) theory of relativity is that all laws of nature have the same form in all inertial frames. Electrodynamics predicts a fixed speed for electromagnetic waves, so light must have this speed in all inertial frames. Fixing the speed of light in all inertial frames while maintaining the relativity postulate requires that inertial frames are related by Lorentz transformations. The Lorentz transformations ensure that there can be only one invariant speed, and they also ensure there is no inertial frame moving faster than the speed of light. They do not mathematically rule out the possibility of objects moving faster than the speed of light, but the existence of such objects would have all sorts of weird consequences (instantaneous action at a distance, backwards causation). The Lorentz transformations do ensure that any object traveling faster than the speed of light will have the speed of light as a lower limit, so if neutrinos genuinely travel faster than speed of light and special relativity is approximately true, we should never observe neutrinos traveling slower than light. Unfortunately, we have.