In the most recent versions of Xcode (and future versions), classes such as UIViewController are not available as separate selections when adding a new class to your project. Instead, choose to create a new Objective-C class, then, on the second screen of the assistant, set the subclass to UIViewController (or whatever you need). From that point forward, everything should match up.
Frequently I question Apple’s changes to the UI, but, in this case, the change makes Xcode a bit more consistent.
Thanks to the readers for catching this!