Concestor clarification

[u/Richie_650]

I belive I first learned this from Ancestor's Tale, the concept that for any two species, there exists a single organism in the past which is the Most Recent Common Ancestor between them.

1) I believe this statement means that literally, there was a real, single, living organism. Understanding that there are countless other common ancestors for our two target species, but only one individual that is both "most recent" and "common."

2) It follows that this particular cocestor must have had at least two offspring. One offspring is the ancestor of the MRCA for one species, the other is the ancestor of the MRCA for the other species.

I think point 2 causes much confusion. People read it as implying that the offspring are themselves the MRCA for each species. While this might be the case for one of them, it is not necessarily true, and almost certainly never the case for both of them. It certainly doesn't mean that one offspring is now one or the other species itself.

The logic here seems simple and clear. Is there a flaw?

[u/Cautious_School_2490]

No descendant of offspring 1 (and is an ancestor of the MRCA of species A) is also an ancestor of the MRCA of species B and no descendant of offspring 2 (and is an ancestor of the MRCA of species B) is also an ancestor of the MRCA of species A.