> I really want to understand the logic that goes on the head of an anti-vax parent

Science denial is fairly common, a surprising amount of the population engages in it at some degree selectively. Depending on your personal belief systems and political persuasions, you may engage in science denial yourself, and if so and you recognize it, you might better understand that logic.

A few common examples of science denial from around the political spectrum:

- Evolution, Darwinism, and Creationism

- Climate change denial

- Age of the Earth

- Sex / gender differences

- Flat earth

- Excess calories causes obesity

- Denial of obesity as a severe health disorder

- AIDS denialism

- Animal consciousness

- Moon landing

There are plenty of other examples, many of which are popular with educated peoples.