This question comes from a false premise.
To say "you can't oscillate an electron at the speed of light" is like saying you can't drive a car at the temperature of boiling water. They're not measuring the same thing. Oscillation is a measure of cycles-per-unit-time. Speed is a measure of distance-per-unit-time. They're different things with different units.
We can absolutely oscillate electrons at the frequency of light. That's how radios work. A properly functional radio is proof that light is electromagnetic in nature. If light wasn't electromagnetic then it wouldn't induce a current in a radio antenna.
"What is light?" is a philosophical question with many different answers depending on the context. That's because a single "thing" can have multiple definitions. You could say the USA is "the country founded by George Washington" or "the nation-state immediately south of Canada" or "the federal republic formed in 1789". All three definitions refer to the same United States of America.
In physics, the word "light" has a well-defined physical meaning. But there's multiple ways of defining that one thing. You can define light as "electromagnetic wave", "photons" or "that stuff a lamp shoots at you". Which definition you use depends on who you're talking to and what you're talking about.