It may be because the tubes (ureters) which send urine to bladder from kidneys,…these tubes periodically push urine forward. (peristalsis)
Kidneys/Ureters on both sides are attached to bladder below. Then comes one urethra. (short in females and longer in men)
The person who is holding then puts pressure backward and this makes the pain come periodically.
Women have bladder close to uterus so they may feel it like period pain. Not sure. It may be that any periodic pain they feel, they associate it with periods.