It wasn't published in Nature; it was published in the Proceedings of the National Academy of Science.

The rebuttal was also not published in Nature, but it was closer, published in Nature Reviews Urology.

I think the main basis for the criticism is that they didn't look at clinical outcomes like infertility or ability to conceive. As a result, we only have a (very robust) report of a relationship between ibuprofen and hormone levels, not between ibuprofen and x, where x is some directly important/meaningful clinical outcome.

Whenever I see blanket statements like this in such studies ~ it's like they're trying to avoid pissing any powerful corporations that profit from whatever we're told to not draw any conclusions about. They don't want to potentially endanger their careers.

Drug companies hate it when a cash-cow drug is threatened in any way. Anything that threatens those profits is a potential target in one way or another. Researchers studying these drugs know just how much power and influence these drug companies have, and so, are afraid of angering them.

The reasoning is simple ~ make a vaguely disqualifying statement that hopefully keeps them in the good books.

Well, except that it's also common that the people who did the study are often well aware of its limitations, and it's the media that's hyping it up to make a better story. Ignoring disclaimers is how the hype gets started.

Understanding people's incentives will often result in reasons to be suspicious, but suspicions aren't evidence and it's not a shortcut for understanding the science.

Ibuprofen is not really a cash cow though as it is now out of patent protection. So while you seem to desire maliciousness I'd venture to say.this is a rather prudent scientific approach. Should all men stop taking ibuprofen on the basis of this one study? No, obviously not.

Well, the reasons are probably explained in the text (which is not open), but I suppose Nature is peer-reviewed