Variance is defined by
$Var[X] = E[(X-E[X])^2]$
where $X$ is random variable, thus a function (and not a value, despite the name) and $E[X]$ is the expected value of the function $X$.
Here I am using $(...)$ to denote a function and $[...]$ to denote a functional (so a function of functions). I found https://www.quora.com/Why-do-most-people-write-E-X-instead-of-E-X-for-the-expected-value helpful to see the difference.
The expected value $E[...]$ is a functional, so its input is not one of the output values of $X$, but the function $X$ itself. The output $E[X]$ of is a real valued scalar.
The input of the outer $E[...]$ also needs to be function, so we expect $(X-E[X])^2 = Y$ to be a random variable (function). Let's further say $X-E[X]=Z$, which would mean that $Y = Z^2$.
Question: What is $Z^2$ supposed to mean? "Square every value of $Z$ and return the resulting function"? Then the output would be at least a function as well. So far, in my experience, the multiplication of two functions is the convolution of the two functions - also a function.
Question: The term $X-E[X]$ says "the function $X$ minus the value $E[X]$. What is a function minus a scalar supposed to be? Note that it is not the "value of X minus the real value" (not $X(\omega)-E[X]$), because then $X-E[X]$ would be real value, meaning $Y$ would be a real value and that cannot be because the outer $E[...]$ functional requires a function, not a real value as input.