Difficulty in Understanding Relativity

Special relativity says: 1. the speed of light in vaccum is an invariable for all inertial frames of reference; 2. the laws of physics are the same in all inertial frames of reference. Then we will find the rest mass of a photon is zero and it takes infinitely large amount of energy to accelerate an object with non-zero rest mass to the speed of light. The derivation is perfectly satisfying.

Since the speed of light is constant, we know that the light itself is in an inertial frame of reference. So, if we attach our standpoint to this frame of reference, everything else is moving at the speed of light! And of course, we knew it for sure that these things all have a non-zero rest mass!

What happened? The transformation from one inertial frame to another (somehow non-trivial?) inertial frame is irreversible. Where does this assymetry come from? Or, did I make some stupid mistake?