Most bright kids understand that evolution is like a branching bush.
That was very useful when we were simply trying to get a handle on what was on the bush. Often, but not always, those structures grew from the same stems. Now that we have at least an idea of what the bush looks like, we want to know how it got that way. Phylogenetic systematics simply tries to unravel the branches that have grown together. It gives the stems and branch points names, regardless of what direction they lead because those are the relations we're now trying to understand.