It’s easier to tell people to just use a rubber when on antibiotics rathern than explain to them that it’s only for some unpronounceable substances for most of the population and have them memorize a list of substances for which it’s safe to go on as usual - azithromycin is safe, amoxicillin is not. They may sound fairly similar to a layman.

It’s because some substances (in this case, antibiotics) mess with the units in your body that process them and prepare them for excretion. They may inhibit or induce them, but these units process a whole load of other stuff. Including birth control, which can lead to less activity from the birth control pills because they’re inactivated quicker (in case of induction) or the biotransformation to the active form is slower (in case of inhibition, for prodrugs that are inactive as is, but have active metabolites, no idea if this is the case for birth control though).

A similar thing happens with alcohol, for example, which is why you should always be honest with exactly how much alcohol you drink or what other drugs you take when talking to an anaesthesiologist, or any doctor prescribing you any sort of medicine, lest you risk ineffective anaesthesia or treatment (the first one is worse imo).