Someone please explain this to me: I get that CNN's are unfit for learning different poses, rotations and such. However, the I don't get the face example at all.

Let's say there is a layer of neurons that, after some convolution and pooling, get some features like "noseness", "eyeness" and "mouthness". Unless the pool size in the pooling layer was big enough to include the whole face in the same pool, the parts are still spatially separate (although lower in resolution than in the original image).

When there is the next convolution layer, isn't it going to learn that "kernels that have eyeness up, noseness in the middle and mouthness bottom are the most facelike", similarly how the earlier layers learned to identify parts?

Am I missing something, or is it just a bad example?