The structure of the economics phrases like "Price elasticity of demand" felt wrong to me when I attempted to connect the structure of it to the structure of the equation (shown below) used to represent what it means.
I suspect that this was confusing to me for two reasons, with the first being less important: (1) I did not yet understand how this equation works in Calculus, and (2) I am a native user of the English language, which leads one to habitually think sequentially from the top left of a thing and proceed on to the bottom right of the thing.
(2) Is quite damning given that (1) would suggest that this is the incorrect way of thinking of it. Consider that this equation is to be thought of as a "rise over run" scenario, with the numerator (above the division bar) dealing with a value of Y and the denominator (below the division bar) dealing with a value of X.
As the X value changes, the Y value might change, too. And in fact this equation and the phrase "Price elasticity of demand" are meant to suggest that we should consider how as price changes, quantity demanded changes.