In the very beginning of Chapter 2 Natural Deduction, page 8, in Jean-Yves Girard's book Proofs and Types (translated by Paul Taylor and Yves Lafont, published in 1989), the author writes:
Natural deduction is a slightly paradoxical system: it is limited to the intuitionistic logic case (in the classical case it has no particularly good properties).
I don't understand what the author is trying to imply here. What are the so-called 'good properties' that happen in intuitionistic case while being absent or no good in classical case? Anyone can explain it?