Possibly because a varying magnetic field creates a varying electric field (law of induction) a varying electric field creates a varying magnetic field and so forth....
But it may be much simpler to think of electrons as jealous little creatures.For example those vibrating in the sun make those inside a chair to vibrate too because they are jealous. The electrons in our eyes vibrate too because they are jealous and we see the chair.
References:
Conceptual Physics - Hewitt
The Feynman Lectures on Physics
Feynman on youtube
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