People who are against the use of vaccines erroneously think they are protecting their children. They also use a specific way to look at statistics. To explain the problem, we shall use the example of a measles outbreak.
Which simply means that people who don't believe in the efficacy of vaccines cannot perform simple mathematics either.
This problem can also be psychological: humans strive for internal consistency. How can you believe something what cannot possibly be true and stay sound of mind. You simply cannot and therefore a psychiatrist might consider labeling your problem 'cognitive dissonance'.
 The Skeptics Dictionary: cognitive dissonance. See here.