Vaccines should be mandated because the testimonials given by parents about how they do harm are not substantial enough evidence.
For instance, anti-vaxxers have concerns that Autism spectrum disorder might be linked to the vaccines children receive, but studies have shown that there is no link between receiving vaccines and developing ASD. There is no evidence that vaccination leads to any type of disorder or serious harm.
It is only in very rare cases that vaccines can cause serious problems, such as allergic reactions.
But in the majority of cases, vaccines cause no side effects.
The benefits of mandating vaccines far outweigh any of the rare instances where vaccines may do some damage; thus vaccines should be mandated.