Measles only needs a population of about 100,000 susceptible people for it to keep spreading. Not to mention that 5 minutes with an infected person is enough for you to get sick if you're not immune. It's THAT contagious.
Some people may tell you, "Well, most of the kids that get measles are vaccinated! Proof that vaccines don't work!" I always say, flip the stats. Let's say we have a community of 110 children. 100 immunized, 10 not. Let's assume a vaccine efficacy of 80%. With an outbreak, we have 30 sick kids - 20 vaccinated, 10 not. 2/3 of the sick kids are vaccinated! BUT, of the vaccinated kids, 20% got sick, compared to 100% of the unvaccinated kids.
I recognize that there are some children who legitimately cannot be vaccinated for medical reasons or because they are too young. But this is exactly WHY everyone else should be. It helps to reduce the numbers below the 100,000 threshold.