A doc holding your balls and asking you to cough checks for an inguinal hernia, where your intestine pushes through the inguinal canal. This canal is much wider in men, hence it being much more common in men.

I am in no position to judge the procedure on a medical basis but know that it is (or was) near universal for potential recruits and has become a bit of a meme.

Your strong reaction to this procedure is something for you to dwell on.