There's a common conviction, rampant among idiots, that things were better in the old days. Food was great before "chemicals" (except for 3rd-world famine but it's unfair to mention that), everyone was fine before vaccination was invented (never mind that smallpox, polio, TB etc took millions every year because it's unfair to mention that too) and anyway, that nice Dr. Westlake says that vaccines cause autism.
Dara O'Briain has it right: "on one side of the argument we have a dentist who studied for ten years and has 15 years of experience, and on the other we have Barry, who pulls his own teeth with a door".
A further consideration is that most of the anti-vaxxers were vaccinated as kids, to which a few of them probably owe their continued unfortunate existence.