yet all that is ever found is species of one type or another.
Here’s a simpler explanation -
Suppose we have the fossils of an early hominid, species “X”. We have another, later species, “Z”. Another is discovered from the time period between them. It has half the features of “X” and half the features of “Z”.
Is neither species “X” or “Z”. It is a newly discovered species - “Y”.
So if someone sees X, Y and Z and therefore assumes that some process cased X to morph to Y, and then Y to Z?
TO --> 
TO --> 