There seems to be the idea that paper is making the claims that the person in the grave was a) female and b) a warrior.
However, they are actually only making claim A, that the person was female. The claim that the person was a warrior was made earlier by the archaeological team.
So, if you think the paper is making both claims, then the professors criticisms seem valid, as they are unconvincing in establishing this was a warrior. However, if you know that they're only making one claim, the attacks on the window-dressing of this being a viking warrior appear totally pedantic (as it ignores the main claim entirely).