Sometimes I make a series of feature classes, then decide that they'd be better in a feature dataset.
So I make the feature dataset, then try to copy the feature classes into it, only to be met with this error:

So, how about reprojecting it for me? It really shouldn't be this hard to move stuff into a feature dataset.
(Also, more annoyingly, is that the feature dataset is created with the same spatial reference (using WKID< no less) as the feature classes, so I really don't get what the problem is here).