The measles vaccine is actually one of the most effective vaccines in the world. According to Greg Wallace, lead of the measles, mumps, rubella and polio team at the CDC, two doses are 97 percent effective against infection.... But in some people, that response just doesn’t happen. No one knows why. Either your body doesn’t produce enough antibodies, or the ones it does produce aren’t specific enough to latch on to the virus and kill it.... even with two doses, you can get some failure,” says Wallace, “whether it’s because the initial response isn’t perfect, or because the response waned in some people.”[1]
The sad thing is that once the numbers of unvaccinated people goes up, really infectious diseases like measles are transmitted to those who have the misfortune of having an ineffective vaccine much more often:
If you have a group of 1,000 people concentrated in a small space—like oh, say, hypothetically, an amusement park—about 90 percent of them will be vaccinated (hopefully). One person, maybe someone who contracted measles on a recent trip to the Philippines, moves around, spreading the virus. Measles is crazy contagious, so of the 100 people who aren’t vaccinated, about 90 will get infected. Then, of the 900 people who are vaccinated, 3 percent—27 people—get infected because they don’t have full immunity.[1]