According to the article "Farré and González think that spending more time with their children—or the prospect of having to do so—may have made men more acutely aware of the effort and costs associated with childrearing".
Another (arguably more positive) reason could be that new fathers formed a better relationship with their child, and be extension felt more fulfilled in that relationship. That could potentially then lead to them not feeling the need to have more children.
Whether the study or data is flawed or not, anecdotally it makes perfect sense. Splitting childcare duties with my wife have given me an excellent relationship with my child, but I’m sure as hell not going to do this shit again.
Another (arguably more positive) reason could be that new fathers formed a better relationship with their child, and be extension felt more fulfilled in that relationship. That could potentially then lead to them not feeling the need to have more children.