TLDR:
The authors of the study are trying to form causal link where one doesn't exist to conclude that males who have children have lower T.
This gives the headline for journalists to write headlines like the original article: "Men's Testosterone Drops Steeply When Baby Arrives" and tradcon-adjacent sites to say things like "Raising human offspring is such an effort that it is cooperative by necessity, and our study shows that human fathers are biologically wired to help with the job."