** If one phylum can't give rise to another, wouldn't all
extant phyla have
to be present in the fossil record all the way back to the
Pre-Cambrian?
There weren't any Chordates in the Cambrian.  Where did they
subsequently
come from, if not from pre-existing phyla?  Are chordates
therefore
synonymous with whatever preceded them?  If new classes can't
arise from
pre-existing ones, why were there no mammals in the Paleozoic
- and where
did they subsequently come from, if not from pre-existing
classes
(presumably reptiles)?

In a phylogeny lets say there is a branching that leads to having phylum A and phylum B at the ends. Who gave rise to who? A common ancestor which may not be a member of phylum A or phylum B. We would just call this a common ancestor. Hopefully a good fossil record can help us make this judgement on what the ancestor wa however this may not be available so we have to make our best inferences perhaps with the aid of genetics.