In special relativity, the inertial frames are just postulated to exist. There is nothing wrong whatsoever with such an approach: they're frames in which objects will move by constant velocities if no forces act upon them. Newton needed pretty much the same thing to define the laws of mechanics. The important point about relativity (both Galilean and Einsteinian) is that if one frame is inertial, other frames moving uniformly with respect to this inertial frame are inertial frames, too.
This is fully analogous to straight lines in the Euclidean geometry. (Inertial frames are just systems associated with observers whose world lines are straight lines in the spacetime - it's really the same thing in a different space.) Some lines on the paper simply are straight lines while others are not. One could also ask what is the principle that selects which lines are straight. Well, the principle is the set of axioms of the Euclidean geometry. One has to have a system that allows us to say things about the geometric objects - and being able to say whether a line is straight is among the "tools" we have to be given. If we describe the geometry in coordinates that we call Cartesian, then a straight line is given by $ax+by+c=0$.
There is no confusion here unless someone deliberately tries to produce it. Asking who dared to make some systems inertial and others not is analogous to asking why mathematics discriminates against some numbers - because some of them are primes while others are not. Well, mathematics discriminates and it has the full right to do so. It's the very purpose of mathematics - and science - to discriminate all the time. Every time we ask a question, we want to hear the right answer and discriminate against all the other possible answers - the wrong ones. The right answer inevitably discriminates - it treats various objects or numbers asymmetrically. No maths or science could work if someone required the permanent democracy between everyone.
In general relativity, the spacetime is curved and a curved spacetime contains no reference frames - or systems of coordinates - in which the space would look flat. It's simply not flat. So there are no exact inertial frames in general relativity. In general relativity, one may only approximate the notion of an inertial system. One possible definition is that an inertial frame is a good approximation for local phenomena around freely falling objects. If an elevator is freely falling, you may call the frame associated with this elevator "inertial".
However, here on the Earth, it is not the usual choice. We usually say that the freely falling elevator is accelerating i.e. non-inertial. On the contrary, it is the non-falling elevator at rest that is inertial - even though it is not associated with geodesics in general relativity. The choice of the falling elevator has the advantage that you don't have to include the gravitational force among the forces that act on the objects inside the elevator. The only thing you have to include is the crash that will kill you: it's not the free fall but the collision with the ground that becomes your fate. :-)
If you choose that the inertial system is linked to the elevator at rest, you have to add the attractive gravitational force to the equations for all objects on the Earth. Of course, that will make your description of high-velocity phenomena etc. a bit inaccurate. But it's simply the case that curved spacetimes - and nontrivial gravitational fields - can't be exactly described by special relativity (and its inertial frames) only. If this were possible, we wouldn't need general relativity. It's not possible and we need general relativity to describe gravity in the relativistic context.
In the broader cosmic context, away from the gravitational field of the Earth or the Sun, the approximate inertial frames can be defined by the freely moving objects. One of them will be the frame associated with the cosmic microwave background - the frame of spheres such that the total momentum hiding in the CMB photons that are crossing the sphere at each point of the sphere's surface is zero. The CMB frame determines not only what is the vanishing acceleration; it also determines what is the vanishing speed.
With this benchmark in place, one may discuss the motion of the Sun (and the Solar System), our Galaxy, galaxy clusters and superclusters where we belong etc. relatively to the CMB cosmic frame. Those speeds are kind of known. But it's useful to recall that these speeds don't really mean that the Solar System frame is far from inertial. It's because uniform speeds don't spoil the inertial character of the reference frame. So even though the Sun is moving relatively to the CMB frame, by a rather high speed, the system associated with the Sun - and properly oriented relatively to some other galaxies etc. - is inertial with a huge accuracy.