What are the laws and issues surrounding *quantifying over sentences?*

Intuition tells me that if we wish to show that $X$ is unprovable in some system say $ZFC$ we might wish under certain circumstances to state that there does not exist a sentence $S$ within the set of all sentences provable in $ZFC$, such that $S$ proves $X$.

Somebody once exclaimed to me "You're quantifying over sentences" as if this was sacrilege. Is it? If so, why?