Since the turn of the century, there seemed to be a rise in antivaccers. Many of the reasons are not based on scientific fact. The vaccine question seems to be based more on emotion in my opinion.
I suspect a large part of the issue is that individuals can see the world around them and can't see a larger collection of data. If you know someone personally whose child became a bit of an oddball right after getting a specific vaccine it's only natural that you'll be suspicious of the vaccine. If your own child suffered something right after vaccination you'll naturally be hesitant to give your next child the same vaccine.
The trouble with such a limited pool of data is that it's impossible to know whether the vaccine was a direct cause of the issue, an indirect cause, or totally unrelated - we just see an apparent side-effect closely following a potential trigger event.
The scientific community, in theory at least, has a collection of far more data points that can be used to help determine whether there is a causal link between the two, also looking to rule out placebo effects. I remember reading an article about the testing of the covid vaccine that indicated the "soft side effects" (the ones that were self-reported and largely subjective, such as aches and soreness at the injection site) were very common but occurred almost as often with the placebo as with the actual vaccine.
That then turns the entire situation into a matter of whether people trust the scientific community to tell them the truth and the whole truth. Probably the biggest problem with the covid situation is that this trust has been damaged, potentially beyond repair. When people lose trust in the scientific/medical establishment it becomes very difficult to persuade them to do much of anything.
