what does it mean to say natural deduction is paradoxical?

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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?