Is this logically/genetically possible? (23&me result)

My son did the 23&Me genetic test and was told that he had a cousin through the maternal line who had also taken the test.

My first thought was, “cool, I know more or less who that must be - my bio-mom had three daughters. Me, and one sister who has no children, and one sister who has has kids. It must be one of the latter sister’s children.”

But then I got to thinking about it … this sister is actually a HALF sister. We have the same mother, but different fathers. There is zero chance that there was some kind of hanky-panky such that we actually have the same father. (She’s half South American and I’m not, and our mother did not even meet my father until she was about 16).

For my son to have a full cousin from the maternal line, doesn’t this imply that the he and the cousin have 2 of their 4 grandparents in common?

(I doubt it matters, but as background: I did the NatGeo test and came up with the T1a1 haplogroup; as one would expect, 23&Me gave my son the same results.)

ETA: from the above one might think: ah, the “childless” sister actually had a kid and gave it up, and that’s who it is. But she is also my half-sister. There is no way in hell I have ANY siblings who are not half-siblings, though I have 9 half-sibs.)

Are you sure it’s a full cousin? 23&me lists a lot of “cousins” for me that are only 1.5% or less shared DNA. That is, they are cousins in name only. My closest relation on the site is “2nd to 4th cousin” with 1.53% shared DNA.

Yep - he’s got several second and third cousins listed, but this is a first cousin.

Yes, it implies that. But what it actually means is that your son and this person has a match close to the statistical average of a pair of people with 2 of 4 grandparents in common. It’s entirely possible, although it’s a lot less likely, for someone to get that close a match with only one grandparent in common.

That makes sense.

Actually, would the offspring of my half-brothers (on my mother’s side) count as well? What about offspring of any of my half-siblings from my father’s side?

If they all count, there are a lot of people out there who might, through a somewhat unlikely but not impossible genetic mix, come up as a cousin-match for my son.

Yes. Unless you’re testing mtDNA, the gender of the contributor matters little.

The fact that it was described as " a cousin through the maternal line" suggests that there was a mitochondrial contribution.

Or that part of the match were on the X-chromosome of two males.

ETA: mitochondrial DNA doesn’t change often enough or have enough variability to tell first, second, 20th cousins apart

That would just show that the line was non-paternal, not that it was maternal. The vast majority of lines are a mix of the two.

For first cousins though …

ETA: Never mind. Evidently I can’t count to two.

has anyone considered that 23&me is not necessarily an accurate measuring tool?

This. Besides, it probably doesn’t have the choice of “half cousin.” It probably can only say 1st cousin, or 2nd cousin. You will share mathematically, with first 12.5% DNA, and 2nd cousins 3.125%, but life isn’t mathematics, and in reality people share a range that probably averages out to about those numbers, but 1st cousins can come almost as close as siblings, or nearly as far apart as strangers*. The test probably looks at which number you are closest to, and spits out that relationship. A half-1st cousin is going to be around 6.25%, but since this is real life, it’s going to be on one side of that number, or the other. If it were 5.5%, which made it closer to the 2nd cousin, it probably would have spit that out, but if it’s 8%, making it closer to the 1st cousin, it spits that out.

And you have to include not only the fact that half-cousins will not have EXACTLY 6.25% shared genes, but also the probability that there is some error in the test. It might come up with a match of 8%, when in real life it’s 7.25%.

At least, that’s my theory.
*My grandmother has an identical cousin, just like on the freaking Patty Duke Show, and I’m not making it up. They are about 12 years apart in age, otherwise, there’d be no way to tell them apart. And they don’t even have a set of parents who are identical twins, or anything.

We could go into how the accuracy depends on how many markers you pay to have examined, and how those markers are highly variable, but could by chance be shared by multiple ancestors, but that’s not all that relevant to the OP’s question. 23&me are offering a reasonably accurate product, and without some evidence of flaws there’s really no reason to raise the question of errors in testing.