Why isn't a Photon justified in concluding that it is at rest and everything else is moving past it at c? Why isn't a photon moving at c not justified in concluding that it is at rest and everything else is moving past it at c since relativity postulates that the laws of physics are invariant (i.e. identical) in all inertial systems (non-accelerating frames of reference)?
Which part did I overlook? 
 A: Your question is the one that Einstein pondered for long time and from which Special Theory of Relativity was born.
He wondered what could happen if you travel at the speed of light how would you see a ray light. The problem was that according to Maxwell's Electrodynamics, explained light as oscillating $E$ and $B$ vectors along space and time, so as a wave. But then you would see $E$ and $B$ oscillating statically, which was not observed in nature thus contradicting experience.
There lies the problem with that reasoning, which lead to admitting that light should be invariant for all inertial systems, and further to STR.
Baring this in mind, you can see why a photon cannot be thought of as a classical particle, and is only a working concept in Quantum theories where velocities and positions cannot be simultaneously known to infinite accuracy, thus paths are inconceivable. 
So not in the scales where light behaves classically, nor in those where it does not, can a photon it be conceived as a standing in rest, because it contradicts observation. 
A: Elementary particles do not have consciousness, individuality or volition. They follow the rules of the boundary value solutions of the quantum mechanical equations they obey. 
The relativistic quantum mechanical mathematics have zero mass particles moving at velocity c, and in all valid frames massive particles move at velocities less than c. It is the  mathematics "xxxx", to use a popular paraphrase. There is no rest frame for zero mass particles and no velocity equal or larger than c for massive ones using Lorenz tranformations, which are imperative for relativistic velocities.
