Alligators-->Reptiles Example

I do not understand how the same example (and same answer) to explain a necessary premise can be used to explain a sufficient premise as well. If the answer to strengthen using a necessary premise was that Alligators are reptiles, yet the sufficient premise is that Alligators are Reptiles too. I understand the reasoning for it being the answer to a sufficient premise but I do not understand how it can be a necessary premise