This is talked about in the article too: You do not have genes from all your ancestors, because any given person only contributes half their genes to their children. So you have to go much further back to find a point when someone's genes would be present in all modern-day humans.

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.

Simple explanation. It is the difference between "things have mixed so much that everyone is your ancestor somehow" and "on a strict matrilineal or patrilineal descent, everyone winds up at the same thing".

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.

Adam and Eve are along the male (or female) line, whereas the common ancestor could be anywhere in your family tree. So 10 generations back you only have a single male line ancestor but 1024 ancestors total.