I think he's assuming that if you (somehow) increase E, mass "magically" increases to match it. Instead, the only variable that can be manipulated here is mass. If you increase the mass, you'll increase the energy.
It would be like if C is miles per gallon on your car (assuming that is a constant*). The variable you can manipulate is the gallons of gasoline you add. More gas, more miles; less gas, fewer miles. You can't say, "Oh, mpg can't be a constant, because if you drove twice the miles, how would you automatically get twice the gasoline in your tank? Magic?"
*Of course, it isn't, but let's say all other variables are being controlled.
The way you get more E is to provide more m. You can't increase E otherwise.