> Those children didn't die from a vaccine, ... They died because of human error administering a vaccine. This is a bad argument and does not work in practice,

> Those children didn't die from a vaccine, ... They died because of human error administering a vaccine. This is a bad argument and does not work in practice, because people perceive it as a language trick. If a child was vaccinated and then died in a result of the process, most people call it "die from a vaccine" independently from the mechanism. Trying to make the risk of the process look smaller than it is by focusing attention on technical details makes conspirologically minded people who do not understand the details even more suspicious. In other cases you mention people go to doctor, because they can clearly see that not going is way more risky. So a better argument is to remind them that if enough people choose to skip the vaccine the danger from the virus will be much higher than the danger of nurse making a mistake.