So like Adam and Eve? :-)
I guess it's kind of like the difference between a permutation and a combination.
In particular, if you have a male ancestor at the Identical Ancestor Point but the lineage from them to you passes through a woman at any point in the family tree, you would not get that male ancestor's Y-chromosome via that line of descent.
Or put yet another way, if you are male, you have 2^N (possibly overlapping) ancestors N generations back, but only _1_ ancestor N generations back that contributed your Y-chromosome. Comparing to a different male, the chance that you share Y-chromosomes is naively something like 1/P where P is the size of the male population at the time, while the chance that you share your ancestor sets is a much more complicated calculation, and the article claims it's ~1.
In the first the path goes through both fathers and mothers. This is easier to achieve, and so you get to it more recently. The second is harder and so happened longer ago.
There was too much time between them.
We focus too much on these two inputs, and forget the other (20) pairs of our nuclei.
And then what would an analogy look for prokaryotes - bacteria, archaea? If my understanding of biology is correct, it would be like an infinitely tall, densely tiered waterfall. There's some forward generational movement, but there's also plenty of lateral ones - exchanging gene packets "at runtime".
Or: it's a DAG, not a tree.
It helps to visualize this more as a mesh than a tree, or as a flowing river. The river divides around rocks and obstructions (those are points of temporary divergent evolution) but ultimately all flows together (convergent ancestry). We are truly one body of genetic material, and yet each is a unique combination of backwards traces.
It's really very cool IMHO.