You should care, it is a big distinction between “named” and “begot” it is the key to the puzzle. To disregard because your mind is set, is in error.
There are five verses which God specifically writes as “named” to distinguish from those names who were simply “begotten”. This is important information you should take into account. (Gen 4:25),(Gen 4:26),(Gen 5:29),(Gen 21:3),(Gen 25:26)
Arphaxad was “begotten” by Shem, which means Arphaxad was a progenitor, a descendant, a grandchild, a great grandchild, a great great grandchild, etc.
in (Gen 4:25), (Gen 4:26) God uses special language to set forth a precedence, to discern between offspring and grandchildren. He is telling us about Seth and Enosh right off the bat, then immediately in Genesis 5, He begins the genealogy account and begins with Seth and Enosh again, setting the precedent between “named” and “begot”.
It is a very very big distinction.