What is wrong is your understanding of epidemiology. Vaccines are not 100% effective, so if one person gets a vaccine and lives in a community where no one else is vaccinated, that one person is going to be exposed to a lot more possibilities for infection, which raises his chances of contracting the disease, even though he is vaccinated. But when a sufficient number of people are vaccinated, the overall circulation of the virus is vastly reduced, benefiting everyone. In addition there are people (like infants) who are too young to get the vaccine. The only way they can be protected is to remove them from society, or to have society be mostly vaccinated.