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On an exam in organic chemistry I was asked why the reaction B proceeds faster than reaction A.

I answered that: in reaction B, I- is a better leaving group than Cl-, the reason being it is a weaker base.

The answer our teacher gave after correcting the exam was: I- is a good nucleophile and at the same time a good leaving group.

I scored 1,5p/2p for my answer.

Are the two answers very different or is there some incorrect information in mine?

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Your answer is simply missing something. Yes, I is a better leaving group, therefore an Sn reaction of an iodide proceeds faster than the one of the chloride. But your starting material in both cases is the chloride. You first need to exchange that chloride for an iodide and that only works well if the iodide is a good nucleophile.

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