Your gut has all sorts of bacteria in it, that help with the digestive process.
Systemic antibiotics, being fairly limited in intelligence, go in spraying bullets at every living micro-organism they encounter. Acne-related, or otherwise. All fall before the Might that is Tetracycline (or whatever).
Since part of your digestive system has been assaulted and is out of operation, your innards aren’t working properly. Hence, diarrhea.
Presumably some folks’ gut microbes have better body armor than others. Or some days they remember to wear their armor and some days they don’t. Or they can handle some antibiotics and not others. All in all, it’s pretty much a crapshoot (sorry!) as to whether you experience this sort of “side effect”.
Us ladies have a related issue that you guys don’t. Some antibiotics mess things up in other parts of the anatomy. Some don’t. 'nuff said?