GE 11:12 Arpachshad [Arphaxad] was the father of Shelah.
LK 3:35-36 Cainan was the father of Shelah. Arpachshad was the grandfather of Shelah.
While it is evident that at least one person supposes that it is inconsistent to say that Arphaxad was the father of Shelah, it is not.
We speak of George Washington as the father of our country. Is he the physical ancestor of us all?
We speak of Abraham as the father of the Jews, and the father of the faithful.
While Abraham has no necessary physical ties to the faithful, he is the father of the Jewish race. Is he the immediate father of them? No. He is the ancestor of them.
So it is with Arphaxad and Shelah.
There’s no inconsistency at all.