So do they really call everyone "cousin?" Why not just use "degree of cosanguinity?"
I think Ancestry does it to be simple. But it often confuses people. They have categories of
Self/twin -- This is if you have tested twice for yourself or you have an identical twin.
Parent/child -- This really is one of those two things. It is the clearest category.
Immediate Family - This is basically full siblings, including fraternal twins
Close Family - On the match page Ancestry says the possible range is close-family - 1st cousins. If you click on what does this mean it shows examples of aunt/uncle, niece/nephew or grandparent. It doesn't show as example a half-sibling which people in this category often are!
People routine see that range of close family to 1st cousins and assume someone in this category is a first cousin when in reality the only way a 1st cousin is in this category is if they are double first cousins (sisters married brothers).
I myself had a half-sister turn up in this category and I did not initially realize that she was a half-sister! On genetic genealogy pages, people routinely assume that someone in this category is a cousin when it is really an unknown half-sibling....
First Cousin - Basically these are people with a DNA cM range of which encompasses a fairly wide range. People at the low end could be 1st cousin once removed. This does include half-aunt/uncle or half-niece/nephew or great grandparent/child
Second Cousin - This really includes a variety of different things as you start having lots of possibilities that fall within this centimorgan range. For example, on my result one of "second cousin" matches is a 1st cousin, once removed. Another is a 2nd cousin/once removed. You can also have a 1/2 first cousin, etc.
Third Cousin - Again, even more variability. Someone in this range absolutely won't be a first cousin. But they could be a variety of different types of removed cousins and could be half second cousins, etc. Also -- this is important -- about 10% of the time you do not share DNA with someone who actually is your third cousin. I have a proven third cousin who is absolutely the son of his mother and full sibling to his siblings. I share DNA with the mother and his siblings, but not him. He falls in that 10%.
Fourth cousin -- More of the same but with fewer DNA. If it is possible to share no DNA with a 3rd cousin it is entirely possible that someone who is a third cousin will fall in this category on Ancestry. And some more distant cousins fall in here.
Distant cousin -- I don't look too much at these matches. I have over 100,000 distant cousins on Ancestry. These matches are more likely to be by chance than the closer matches.
It's obviously a crap shoot. I'm convinced we have the same parents, grand parents, all the way back to forever, yet one sib of 4 was told there was native American in her genome and three didn't get the indicator. I still say it's got to be wrong for one or three.
It could be wrong it doesn't have to be wrong, particularly if the share of NA DNA is small. It could be that the rest of you just didn't inherit it. As mentioned above I have a documented 3rd cousin (documented because I have seen his DNA match to his mother and siblings). He is the son of his mother and full-sibling to his siblings as proven by DNA. He is my third cousin. I share DNA with his siblings and his mother ... but not with him. Nothing is wrong. He just didn't inherit from his mom the part of her DNA that I share with her. His siblings did.