Ok, of course light doesn't need a medium. But is this really true?
Many waves like sound and water waves are just motions of a medium, so can light also be just the motion (excitation) of an electric and magnetic field?
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Yes and no. It depends on how you define medium. Light is an electromagnetic wave, and you are right in saying that light is the excitation of the electromagnetic fields. When people say "light doesn't need a medium", they mean that light doesn't need a material medium. This is something that truly baffled 19th century physicists, because they only had experience of water waves, sound waves, etc. which needs some bulk material to propagate.
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At present physics postulates that the underlying framework from which classical physical theories emerge is quantum mechanical, and described by the standard model of particle physics which has a number of elementary particles and three interactions between them.
So the classical electromagnetic waves that are described by Maxwell equations emerge from a confluence of innumerable photons, elementary particles in the particle table of the standard model .
Photons carry the information of the electric and magnetic field they will build up, in their wavefunction which is a solution of a quantized maxwell's equations.
So as far as the classical framework there is no medium. Considering the underlying quantum mechanical framework one may handwave that classical light rides on innumerable photons. This link shows in quantum field theory how the classical fields are built up from the quantum mechanical ones.
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