This question was closed for lack of clarity. Although it's a bit awkwardly worded, I think the clear intention was to ask "Why does the speed of light show up in an equation that relates mass to energy?", which seems like a reasonable question for someone who has not studied relativity. I think it should be reopened.
The question has "Not speed of light" in the title, and later says
I’m not talking about the math working out, or why it needs to be $c^2$. But rather, what is the nature/essence of light that allows it to be a conversion factor?
I don't understand what that means. It seems to be specifying that it is not about why the speed of light appears—but rather about whether there is something intrinsic about light itself. However, since it is the speed of light, not "light" in the abstract that appears in the equation, I don't understand what the querent is trying to ask about. So it does not seem surprising to me that other users voted to close the question as unclear.
Please help me! I’m not stupid, I just need some help. I’m a medical doctor not a physicist. I’m new here and I don’t understand why I keep getting shut down? My question is basically: “Why does the speed of light show up in an equation that relates mass to energy?" I don’t understand why this phrasing is more elegant. But YES this is what I want to know. What should I do now? I have asked this question to many cosmologists, mathematicians and physicists. Everybody relates it back to making the math work. But I think I’m asking a more profound question. Thanks Peter I really appreciate your understanding.