I think it's good to question things, I'm a big follower of "question everything", don't take anything as fact, from any side, though we do have to make assumptions that those who know what they are talking about know what they are talking about. In philosophy we are taught Descartes, that we can't ever truly know anything, what is knowledge even? He tries to make sense of the world, but realizes everything comes from our senses which can be fooled, so really we can't trust anything. Then at least he says we exist, we can trust that, and build our knowledge base back up from that one tiny fact, that because we clearly are having thoughts we must exist, that can not be doubted.
Personally after I take the risks into account for everything I feel the risks of a severe reaction are less than the risks of a severe reaction from the disease itself, so it's worth it to get the vaccine. For some vaccines like the flu I don't particularly agree to the same statement, unless you are working with the young or old, or those who might be at any kind of risk from the flu. We all have our choices to make. There's always that one in hundred million horror story you hear, and you as a parent don't want to be responsible for that. For some reason we as a whole feel more responsible for our actions than our inactions. If my action will do the same thing as my inaction, I would feel more guilty if I had done it, then if I hadn't. I think because if I hadn't it would feel inevitable, while if I do act I feel like a catalyst.