All feature classes within a feature dataset must have the same privileges. This is by design. Therefore, it is not possible to grant different privileges to feature classes within a feature dataset.
The role of a feature dataset is to group topologically-related feature classes. Therefore, a user must have uniform privileges on all feature classes in a dataset. For example, it would not make sense to have edit privileges on a feature class of electrical lines but only read privileges on the poles to which they are connected in a network.
The feature dataset plays an important role in managing privileges. By design, the feature dataset enforces that all feature classes it contains share the same privileges; this is contingent on managing privileges through ArcCatalog, which is required when working with a geodatabase. For example, if in ArcCatalog a user right-clicks a feature dataset and selects Privileges, ArcCatalog will automatically grant privileges to all feature classes it contains. The converse is true when revoking privileges from a dataset.