I think that part of the issue is that many people do not typically know how to differentiate between scientific, peer reviewed, statistically significant research and data vs a claim that doesn't have associated data.
For example, person A might say "Joe Smith died after being vaccinated". Which may or may not be true, but the question becomes, is there statistically significant data to suggest that the person died due to the vaccine vs simply dying of natural causes?
Same goes with miscarriages during pregnancy. Most adults are well familiar with the fact that infertility and miscarriages are relatively common. Most people have either experienced a miscarriage or know someone who has, before the pandemic even began.
So if someone experiences a miscarriage after being vaccinated, They might be led to believe that the vaccine had something to do with it, although if we look at general statistics we might see that it were something that would naturally occur with or without a vaccine.
And I think a lot of people struggle between understanding the difference between correlation and causality, and aren't familiar enough with the scientific method and peer review to know how to look at data.