I forgot to answer this:
"Statistically the risks are much smaller than the harm the diseases can do."
Listen up. Here comes a brief lesson on Probability vs Risk (they are not the same thing):
Risk = Probability x Outcome
... which means the Probability of something happening might be very small (say, 0.01%) but the Outcome might be so bad (say, death could be valued at -10,000,000) that it would be a high-risk event: Risk = 0.1% x -10,000,000 = -1,000.
What you mean by the sentence above is that the Probability of vaccine damage is lower than that of catching, say, Mumps. But vaccine damage means permanent damage to the body and brain, severe blow to quality of life (say, Outcome = -1,000,000) whereas Mumps will probably just mean two weeks of discomfort, or if complications arise, limited to something far easier to live with than brain damage (say, Outcome = -1,000).
So (making up the numbers here to explain possibilities of calculation) the Risk of getting the disease, where Probability of getting it is 5%:
Risk = 0.05 x - 1,000 = -50
... and Risk of vaccine damage, where a much lower 0.01% Probability of getting vaccine damage:
Risk: 0.0001 x -1,000,000 = -100 , where Risk is larger although Probability is smaller.
You see, of course, that these numbers are subject to change according to personal assessment - for example, some people might think permanent brain damage is a fate worse than death, in which case their perceived Risk would be even higher.
I hope that explained the difference between Risk and Probability, and showed you why you are wrong to assume that low probability = low risk.