Although their are many valid reasons to avoid the use of vaccines under certain circumstances, there are many invalid reasons that advertise false benefits to avoiding vaccines.

Throughout the entire history of their existence, ever since Edward Jenner innoculated individuals with cow pox virus in order to provide immunity against the deadly small pox virus, their has been opposition to the use of vaccines [1].

A great deal of the opposition comes from the fact that the benefits vaccines confer to people and entire populations are not readily visible. Most drugs, like antibiotics or antihistamines, relieve their users' symptoms shortly after they are administered. On the other hand, vaccines are given to healthy individuals [1] in order to ward off disease, so if an individual gets vaccinated for influenza at the begining of flu season and gets through the entire year without contracting the illness, there is no concrete proof that shows that they were effectively immunized by the vaccine, as opposed to just being lucky enough not to get the disease. The benefits of vaccination do become apparent on a population-wide basis, when data is compared between countries that had high levels of vaccination to those that did not. Countries whic had lower opposition to the use of pertussis vaccine (Hungary, Poland) had substantially lower rates of the disease than countries which had strong opposition (Sweden, Russia) [1].

Modern-day opposition to vaccination was significantly exacerbated in the late 1990s, when a British medical journal known as The Lancet published a paper written by Dr. Andrew Wakefield, a physician from the UK [2]. Wakefield claimed to have found a link between the MMR vaccine and the autism, which has fueled widespread public mistrust of vaccines. Although this link has been heavily studied and debunked by multiple studies that followed [3] (this culminated in The Lancet formally retracting the original paper in 2010, when it referred to Wakefield's work as "the most appalling catalog and litany of some the most terrible behavior in any research"). Nevertheless, the effects of Wakefield's paper linger.

Sources

[1] Dr. Tapping's Lecture podcast

[2] http://arstechnica.com/science/2010/02/the-lancet-retracts-paper-linking-mmr-vaccines-and-autism/

[3] http://arstechnica.co.uk/science/2015/10/vaccine-safety-tested-again-by-injection-into-infant-macaques/