The problem with risks and probability is that human brain does not process probability numbers well, so it is all or nothing.
Anti-vaxxers point of view: I do not understand what 0.0001 is, round it up to 0.5 - OMG vaccines kill.
Vaxxers point of view: I do not understand what 0.0001 is, let us round it down to 0. Vaccines are harmless.
Second point is way more rational, although of course also incorrect.