According to a google search, the definition of a medium in physics is the substance that carries a wave. The definition of a substance in physics is matter with specific composition and properties. The definition of matter in classical physics is a substance (this is confusing. Is substance a type of matter, is matter a type of substance, or are the two terms interchangeable?) that has mass and takes up space.
So an electromagnetic field meets the definitions of both substance and matter. As a substance, it has a specific composition as it is made of an electromagnetic field (the most fundamental entities are made out of themselves) and it has well defined, specific properties. As matter, it produces a gravitational field and hence has gravitational mass, and also has inertial mass, as seen here: https://en.wikipedia.org/wiki/Electromagnetic_mass
It also occupies space.
Given all this, why isn't the electromagnetic field accepted as a medium for electromagnetic waves by the scientific community?
Note: the aether theory had a substance pervading all of space as an absolute frame of reference and medium through which electromagnetic waves traveled, and movement relative to it (such as earth's orbit around the sun) would cause the speed of light to change.
The special theory of relativity removed the need for an absolute frame of reference, as light (and all massless entities in general) always move at c, regardless of movement relative to them.
But I do not understand why this removed the need for the electromagnetic wave to have a medium. Special relativity removed the need for aether as an absolute frame of reference, but it did not disprove of it, and by pure logic, a wave must have a medium to propagate at all, right? So can we call the electromagnetic field an 'aether' for electromagnetic waves?