Well, its an historical fact that he was not a Pope.
First, in order to prove the reality of His human nature, in contradiction to the Manicheans, who said that He had an imaginary body: and in contradiction to Apollinarius, who said that Christs body was consubstantial with His Godhead; and in contradiction to Valentine, who said that Christ brought His body from heaven.
The reason that we don't worry about this now is because people like Thomas Aquinas, Albertus Magnus etc already did all the heavy lifting.
We know that Jesus Christ is True God and True Man. He was not a phantom; neither was He a mere human with a Divine brain, nor was He one of half-a-dozen variations on the same lame theme. He was - and is - and ever shall be - Incarnate God.
Half-bright moderns dismiss Thomas, thinking muddy thoughts about angels and pins. But where would we be, if we still had to argue whether or not Christ was God every time we talked about Him?
Thanks for sorting that stuff out, Thomas!