Special relativity: why moving refrence frames? The idea that one refrence frame(RF) is moving relative to another is extremely counter-intuitive for me. since I always think if one thing moves and the other is stationary then they share a common stationary RF, while one thing itself is physically moving relative to that RF. hence I see no reason to creat two separate RF. Is there any advantage in considering moving RFs rather than moving physical objects?
 A: 
Is there any advantage in considering moving RFs rather than moving physical objects?

Recall W. Rindler's characterization:
"An inertial frame is simply an infinite set of point particles sitting still in space relative to each other."
Reference frames in general are to be thought of as sets of (perhaps idealized, and only hypothetical) identifiable physical objects (a.k.a. "material points", "observers", "participants") who are (thought of as being) (primarily) capable of determining their geometric relations between each other, and (secondarily) to record and report their meetings (in passing) with participants who belong to other reference frames.
Therefore, if it is intuitive to you that physical objects may be moving wrt. each other, you do thereby already have the intuition that constituents of (different) reference frames may be moving wrt. each other.
A: If I understood you correctly the idea of moving Frames of Reference looks counter-intuitive for you because you feel there is one Frame of Reference which is "actually" "truly" stationary, and if other things are moving in this RF they are "truly" moving, otherwise they are "truly" at rest.
Imagine you are in a spaceship somewhere deep in space. How can you find out if your spaceship moving or not? You can measure distances to stars, but stars are moving themselves. Some of them are getting closer to you, others farther. You feel like you are at rest. To describe what is going on on your spaceship it's very convenient to use RF where your spaceship is at rest. Ok.
And suddenly another spaceship flies nearby. Inhabitant of the other spaceship uses RF in which HIS spaceship is at rest.
And there is no way to tell which RF is better.
Inhabitant of the other ship describes some process which takes place on his ship using his favorite RF. Like "there is a ball jumping on a floor, 1 jump per second". And if you really want to describe this process in your RF, you have no choice but take the description of the process in the RF which you think is moving and translate this description into the RF you like more.
A: An RF is not the same as a set of global (universally agreed coordinates). I can be moving in my own set of coordinates,  measuring both objects inside my space ship and making  astronomical observations of goings outside my ship. I can choose any coordinate system I want and  it will always move along with me, I will always be at the origin of it.
If I can do that, then so can someone else, going in the opposite direction, with themselves at the origin of their chosen coordinate system, that moves along with them.
So there is no overall coordinate system for both of us, the same idea as there is no absolute space and time measurements that we both agree on. 
But using the Lorentz transformation, we can reconcile each others measurements, because the physical laws are absolute, even though space and time measurements are different for observers in different reference frames.
