The issue is not just risk to vaccinated children, but risk to the legitimately unvaccinated - too young, immunocompromised, any other condition that's scientifically known to make vaccination unsafe. Those people can't rely on vaccination, so they must rely on herd immunity. When herd immunity weakens beyond a certain point, those people are completely vulnerable for reasons that have nothing to do with their own choices. When we talk about the freedom of some people to forego vaccination, we're talking about taking away these other people's freedom to participate normally in society without significant risk of contracting an often crippling or even fatal disease.

Other scenarios have already been given, but one risk to be considered is younger siblings of classmates who are not yet vaccinated.

Not far from where I live, a 3-month-old baby died of whooping cough. The DTaP vaccination against pertussis is given at age of 3 months, so the baby had no immunity yet; some scolded the baby's parents for being anti-vaxxers but that was cruel - they were simply following the standard vaccination schedule. The legitimately not-yet-immunized baby was killed by being exposed to someone who most likely had refused vaccination. This is difficult to prove, of course, and case details are not public.

Here is a concrete example. MMR is two dose regiment. The current anre recently updated CDC recommendation is that if a child experiences thrombocytopenia within six weeks after the first dose to not give the second dose. Thrombocytopenia is usually not serious - nose bleeds, easy bruising, bleeding of the gums - but since the risk is higher for those that experienced that side effect after the first dose, that is why it has become the recommendation.

One dose of MMR puts their effective immunity to measles at something like 85% during childhood. It varies with how strong the immune system is when the first dose is given, most children get it at six to nine months. At nine months one dose is 85% effective and at 12 months 95% for most infants. It is presumed that the effect is smaller in those vaccinated at six months and those that experience thrombocytopenia and the recommendation is relying on 95% immunization rate for herd immunity. Something like one in 25K children are in this category. There are other categories of people not immunized as well.

Not all children are able to be vaccinated for medical reasons (allergies, weak immune systems/cancer). They could also potentially carry the disease to children who aren't old enough to be vaccinated yet.

Vaccines increase individual resistance to infection, but they do not increase it to 100%. However, when a group is all vaccinated, the effect is that transmission rate drops below what is needed for a disease outbreak, and thus the group gets near 100% protection.

A cluster of unvaccinated children in a group create a living habitat for small outbreaks, lengthen exposure time of vaccinated kids, and thus create the conditions for the extra vaccine protection to get pierced.

Vaccines aren't 100% effective.

In the recent Disneyland/California measles outbreak, 5 of the infected were considered vaccinated against measles.

http://www.cdph.ca.gov/Pages/NR15-008.aspx