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Full Idea
To put the predicate letter 'F' in a quantifier is to treat predicate position suddenly as name position, and hence to treat predicates as names of entities of some sort.
Gist of Idea
Quantifying over predicates is treating them as names of entities
Source
Willard Quine (Philosophy of Logic [1970], Ch.5)
Book Ref
Quine,Willard: 'Philosophy of Logic' [Prentice-Hall 1970], p.66
A Reaction
It is tricky to distinguish quantifying over predicates in a first-order way (by reifying them), and in a second-order way (where it is not clear whether you are quantifying over a property or a unified set of things.