Vaccination is a super complex topic, so I'm afraid of commenting on it and saying something stupid.
I understand some of the anti-vaccination arguments/thoughts people can have, because like ThunderKeil described, choosing to administer a vaccine to your kid, for instance, feels like the responsibility is on you if there's a side effect. Those thoughts are related to the fact that when you have to make that kind of decision, the perspective is that of yourself, your family etc. not that of society as whole. You have to play good-cop-bad-cop in your mind about there being a super low chance vs. vaccination being overall more effective the more people do it vs. the severity of the disease itself, etc. (I'm not talking about extreme anti-vaccination people who think Bill Gates putting chips in your body, but about people like my mom, who just don't know what to think and are afraid of what they don't understand but have to make decisions on)
As an example, when I was a kid the chickenpox vaccine wasn't a thing in France. So when a doctor ignored our questions on the vaccines and gave the chickenpox one to my son without asking us, even though it wasn't on the list of mandatory ones, I was upset, because I got chickenpox and in my experience it was a non-event in my life, and likely boosted my immune system anyways. For that one vaccine, I would have opted out because of my perspective on it (even though I'm sure there's a case to be made that there's still one in millions of chances to get a bad case of chickenpox that leads to complications).
Science on the other hand looks at the high-level perspective and for sure vaccines are great when you look at numbers. They save or improve countless lives. But that also means that in my experience (cue that same doctor I was mentioning for instance) people who look at it from the scientific perspective tend to accuse and shame people who see vaccines from another perspective, instead of understanding where those people are coming from -- which I'd argue usually turns people off even more. There's so much stuff online about how not vaccinating is like a crime, but I haven't really seen any that tries to discuss (instead of shut down) the fear of being that one-in-a-million case, the responsibilities we have to our kids, the fact that vaccines do have side effects from mild to grave (which often gets brushed off because numbers, but must really hurt the people that did suffer bad side effects themselves or their relatives) etc.
To go back to the chickenpox example again: from what I could gather at the time, the chickenpox vaccine doesn't fully protect you (only some strands), needs to be done multiple times throughout your life even though getting chickenpox is supposed to protect you for life, and getting chickenpox later in life can be dangerous (so forgetting to get a new shot later in life can have big implications like going sterile for men). This is definitely not a black or white situation where one should just get the vaccine and shut up, but it feels like questioning whether one specific person in a specific country could maybe consider that getting chickenpox early is better than choosing to get the vaccine throughout their life categorizes you as an anti-vaxxer who just hates science and is slowing the progress of civilization.
I feel like vaccination is akin to politics these days, in that there's no actual dialogue happening, it's either you see it my way or screw you, and that's kind of a pity for the people who just have questions and concerns in the middle and aren't trying to dismiss science altogether, but want to make the best choices for themselves or their loved ones.
Anyways, I got my first Pfizer shot a few days ago, and only had a sore arm for about 24 hours. It's contributing to a feeling that this shit will end at some point, before that it still felt a bit unreal.