Why there is a preference between different reference-bodies? I know a classical mechanics law points out the following (Newton's first law): material particles with constant velocity will continue to move uniformly in straight line. If material particles are in a state of rest they will continue to be at rest. This law is just valid for some kind of reference frames (RFs) (to be more accurate, it is just valid for RFs with certain singular states of motion).
The first question coming to my mind was:
Why are there valid and invalid reference-bodies in classical mechanics? I know Newton's laws are just valid at inertial reference frames, but the same question came to my mind: why?
Doing some research I read Einstein thought it was not possible to find the reason why bodies had different behaviours considered with respect to different reference systems (using classical mechanics). Also I read Newton tried to invalidate this preference but it was not possible. 
 A: Although for simplicity Newtonian Mechanics is usually introduced in the language of inertial reference frames, it can also be taught in a coordinate-free way using the tools of Differential Geometry, which is a subject based on the concept of a manifold (a generalization and formalization of the concept of a surface). 
In this more sophisticated setting, spacetime is represented by a manifold, and Newton's 1st Law says that an object free of any forces will follow a straight line in this manifold. In this context a 'straight line' is defined in terms of the manifold, and not in terms of a preferred choice of coordinates.
As you can probably guess, this language follows over into relativity theory in which Newton's 1st Law remains true, with the main change being the geometrical structure of the manifold.
If this doesn't make much sense to you, then you'll understand why people usually introduce Newtonian mechanics in the language of a coordinate system (specifically, one in which a straight line has the simplest possible formula).
Of course, even in this coordinate-free representation one could also ask 'What's so special about straight lines?', and this is something which we take as an axiom, since you have to start somewhere, right?
Your question is important because coordinates are not intrinsic to nature, and shouldn't be essential to stating the fundamental laws. Indeed, that's why Differential Geometry is such an important subject in physics.
