What makes the disturbance in Electromagnetic waves move? I get that changing electric field will have a curly changing magnetic field and changing magnetic field will have curly changing electric field. So when we move a charge up and down, electric field will change, which will produce this changing magnetic field and this changing magnetic field will inturn produce new changing electric field. I get till here. Where I am stuck is why should this disturbance move? charge is not travelling. It is simply oscillating. Shouldnt the changing electric and magnetic field be localized? I know I am missing something very basic here but unfortumatley not able to put my finger on it.
 A: The general description of dipole radiation is a follows: There is an electric dipole in an antenna (hence an electric field). The charges switch, so their is a current--that makes a magnetic field, until they have switched. Now there is an electric field with opposite polarity. Repeat.
You can find the description in many places. The problem with it may be related to the problem you are having (intuitively): that it is a description of near-field behavior. The electric and magnetic fields are out-of-phase and do not propagate. (These are the $1/r^3$ terms in the dipole formula: https://en.wikipedia.org/wiki/Dipole#Dipole_radiation).
Now there is a $1/r^2$ term in-which the fields are in-phase, and that is radiation. The points being: 
$1/r^2$ is radiation.
The in-phase nature of the traveling waves is exactly as you describe it: the time derivative of one field couples to the curl of another field (and the curl of a field is the antisymmetric combination of each derivative a one component with respect to a perpendicular component--so the whole thing has a beautiful geometric symmetry to it).
I think it's a little more difficult to intuit radiation from the description of moving charges because intuition describes near-field effects--so you have to rely on the math to discover the radiation term.
A: First, let me change your thinking and turn it the way around, and the question will seem self-explanatory.
It is a common misconception to think that movement in space is not connected to movement in time. But it is. Particles that move in the time dimension (particles with rest mass) have to move in space with speed less then c. Particles that do not move in the time dimension (particles with no rest mass, photon, graviton) will move in space with speed c.
it is a common misconception too, that rest mass and movement in time are not connected, but they are. Particles with rest mass move in the time dimension, and move in space with speed less then c. Particles with no rest mass, photons and gravitons do not move in the time dimension, and move in space with speed c.
Now let me turn your thinking around. You would think that propagation of EM radiation, that is photons need some kind of reason like when you speed up a spaceship to speeds near speed c. But the speed c is the only speed and to slow down in space, you need to gain rest mass, and start moving in time, and start experiencing time like we do.
First, at the big bang, there was a sea of photons, and they all propagated at speed c. Now they did not move in the time dimension and they did not experience time as we do. At the baryon genesis, and asymmetry, heavier particles, with rest mass were created. Now think about a photon box. the box itself is massless, and the photons in it do not have rest mass either. But the box does have rest mass, and it is because photons bounc off the walls and exert pressure on it. So when you confine energy, it will have rest mass. There is no consensus on this, but you could think of a particle with rest mass like energy confined, like an electron with energy (photons, and gluons for quarks) confined, having rest mass.
Now these particles with rest mass travel in space with speed less then c, they slowed down, but in the time dimension they started to move, they experience time.
Now you are asking how the photon propagates. The photon itself as it moves from emission to absorption, its spacetime distance is 0. basically for the photon, the emission and absorption happen at the same spacetime point. The photon does not experience time. It propagates in space with speed c from our viewpoint only. Its worldline is lightlike.
There is no such thing as the frame of the photon, or the viewpoint of the photon. But the universe is set up so that anything with no rest mass, will have a worldline that is lightlike, and along its way, the spacetime distances will be 0.
So anything that does not have rest mass, propagates at the speed c from our viewpoint (who have rest mass), but the photon itself does not need a medium to propagate. The photon itself does not need (extra) energy to propagate, because the universe is set up so that anything that has no rest mass will seem to propagate at speed c in space. It is only when you think of it like a macro object or a particle with rest mass, is that you think you need extra energy to speed up. The photon does not need to speed up, and it does not need a medium. The universe is set up so that from our viewpoint the photon will seem to propagate in space at speed c. But contrary to when something with rest mass that tries to propagate in space, the photon propagates because the universe is set up so that it will go along a lightlike worldline.
It is only because you look at it in 3 dimensions, that it seems to propagate in our viewpoint. In spacetime, four dimensions, the photon travels a spacetime distance 0. So in spacetime it does not really propagate in the everyday way we think of it. It only seems from a 3 dimensional viewpoint that it does. It is more that the universe and the fabric of spacetime and the dimensions themselves extend so that the photon seems to propagate in an everyday sense in 3 dimensions.
A: I think that it is a natural property of the universe, just like how a disturbance of the water at one point in a lake spreads out to the whole lake.
