I've seen various arguments from people who are against vaccinations:-
1. Vaccinated people can still catch the diseases for which they've been vaccinated, therefore vaccinations are ineffective.
2. Vaccinations can damage people.
3. Vaccinated people can shed viruses, infecting others.
4. Morbidity & mortality rates fell dramatically before vaccinations were introduced, therefore vaccinations are unnecessary.
5. Vaccines cause Autism.
1. Vaccination can't stop people from being infected by viruses. What it does is give people a much milder form of the disease so that they produce antibodies to the modified virus. If/when they are subsequently infected by the full-strength virus, their bodies have a much faster immune response to it, much reducing morbidity & mortality and much reducing the chance of infecting many others. See https://en.wikipedia.org/wiki/Vaccination for more detailed information.
2. As everyone is different, some people don't produce any/enough antibodies to the modified virus and have to be re-vaccinated. Most people produce the correct response, which may make them feel mildly unwell. Some people have a bad reaction to the modified virus, which may make them very ill and in very rare cases may damage them. If someone is damaged by a modified virus, a full-strength virus would either damage them much more, or kill them.
3. When people are infected with an infectious virus, there's a period of time (the incubation period) during which they shed the virus and infect many others before symptoms appear and they are then isolated from others. This is why vaccination rates need to be high in order to achieve "herd immunity", to minimise the full-strength virus rapidly spreading through a dense population, or other populations due to rapid transportation. Should modified viruses be shed during the incubation period after vaccination, it's not a problem unless it infects immunocompromised people (who would be much more adversely affected should they be infected by full-strength viruses).
4. Yes, due to improved health care, but there was still higher morbidity & mortality due to catching full-strength viruses back then than there are now from being vaccinated with modified viruses.
5. Association doesn't prove causation. See Vaccines and Autism: A Tale of Shifting Hypotheses. If anything....
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