I was trying to describe ToE in terms of data analysis.
Science idealizes. We say that the temperature is a real number. But when I read a thermometer I only get a range of possible values, due to the presence of measurement error. If we take statistical thermodynamics seriously, then there is no exact real number for a temperature, at best there is a probability distribution. Still, the idealization works well and is simple to apply.
In the same way, the idea of a tree of organisms is an idealized picture. The data is usually blurry, giving an approximate location in the tree. We typically collapse a whole species into a blurry spot in the tree.
But the idealized picture still explains how the prediction works. The consequence of blurriness is that if the data is blurry, then the predictions are blurry.
You seem to suggest that I can tell ancestry by knowing who gave birth to who. How does that technique fit into the bigger picture you gave at first?
This is the crux of the creationist-evolutionist debate.
The tree we can build from "who gave birth to who" is a local tree. Based on reproductive biology, we can see that every organism fits into such a small local tree.
Side note (for the lurkers): I should clarify that "tree" is being used here in the mathematical sense (from graph theory), not the thing growing in your back yard.
What reproductive biology cannot tell us, is whether there is one huge tree containing all organisms, or there are multiple disconnected trees. ToE claims a single tree, and creationists claim multiple small trees. That's their argument of "micro-evolution but not macro-evolution".
If there are multiple disconnected small trees, then prediction should work as I described it within any of those small trees. But there is no obvious reason to expect prediction to work across trees. That prediction works quite well overall, is therefore strong evidence for a single large tree.