Suppose that some relation satisifies a non-trivial functional dependency of the form A->B, where B is a nonprime attribute.
2NF is violated if A is not a superkey but is a proper subset of a candidate key
3NF is violated if A is not a superkey
You have spotted that the 3NF requirement is just a special case (but not really so special) of the 2NF requirement. 2NF in itself is not very important. The important issue is whether A is a superkey, not whether A just happens to be some part of a candidate key.