How do stacked CNN layers work?
I think you might be misunderstanding the phrase &quot;extract&quot; here. Think of it as &quot;gets activated by&quot; instead.
For example, the &quot;nose filter&quot; gets activated by inputs which look like a human nose (more precisely: it gets activated by activation maps of previous layers which correspond to a nose in the input image). And simply put, the following higher level feature maps in your example, which might encode a human face, then get activated if the previous layers contain activated feature maps for a human nose, mouth, eye etc. This article explains it well.
As NNs in general, this process is loosely inspired by how visual perception in humans and other animals works.