The easiest way to promote a conspiracy theory is to take a grain of truth and blow it out of sensible proportion. This is exactly how one of the most pervasive sources of covid-19 vaccine hesitancyāmisinformation about its impact on womenās fertilityāspread.
When women of reproductive age started to be vaccinated in large numbers in the (northern) summer of 2021, some noticed that their periods following vaccination were later than normal. By September of that year, there were more than 30,000 reports to Britainās medicines regulator alone of late periods following covid vaccines (with the true figure presumably higher, because of underreporting). Anti-vaxxers then used this phenomenon to scare women with speculations about long-term damage to their fertility.