The reason why they are called flushable wipes if you can't flush them is because there's no clear standards for what constitutes a flushable wipes and so companies don't have to prove their wipes are flushable.
Companies can also use their own definitions of flushability and most wipes fail the flushability test.
The wipes can be marketed as flushable as it can increase sales because some people prefer to be able to flush wipes down the toilet even though they should not be.
I've flushed flushable wipes down the toilet before and it caused no issues with my toilet or sewer line.
However if you're on city sewer the flushable wipes can get clogged in pumps and screens at the sewer treatment plant.
Also if you have a septic tank the flushable wipes could fill up the septic tank and cause a back up and clog.
Flushable wipes are also typically made of non-woven plastic-free materials which are typically fibrous organic materials such as cellulose.
These biodegradable substances are expected to degrade quickly in the sewer although they don't always do so.
Non-flushable wipes often contain man-made fibers such as plastics for added durability which don't break down in the sewers.