Assuming you're referring to [1] or [2] or [3], it doesn't look like a debunking to me so much as healthy scientific debate, specifically between the Seshat and DRH projects who are both competing for limited resources-The John Templeton Foundation funds both for example.

In such a case the criticism of not being a professional historian seem odd, as the credentials of Edward Slingerland and Bret Beheim, the lead authors of the critical papers, seem to be fairly comparable to Turchin's.

[1]https://psyarxiv.com/jwa2n/

[2]https://eslingerland.sites.olt.ubc.ca/files/2019/09/Historia...

[3]http://peterturchin.com/cliodynamica/what-came-first-big-god...