Thanks Robert. I agree, most of what we deal with are the leaves. It's great to be able to see the structure but it's not necessary most of the time. I guess my argument is that we're calling some of the leaves "branches" instead.
To use a different example I shared with Walter Whiteley in a parallel thread, imagine if we showed kids pictures of Saint Bernards exclusively with the label "dog" for the first 7 years of their lives. Then trying to convince them that a Chihuahua is a "dog" too will be a difficult process. Yet that's what we do with quadrilaterals all the time - no wonder everyone gets confused!