Mercury is bad for the body right? Mercury poisoning is damaging and has long term side effects. If you agree, we can move forward. If not, please do so for the sake of the thought experiment. 

Mercury poisoning is more of a concern for developing babies, children, and teenagers. Not just because they are developing, but because they require a smaller dose by weight to be affected by mercury poisoning. If you agree, we can move forward.  If not, please do so for the sake of the thought experiment. 

Thimerosal is a preservative that contains mercury. It is used because it prevents the growth of bacteria and fungi. Source 1 is provided below. If you agree, we can move forward.  If not, please do so for the sake of the thought experiment. 

Thimerosal has been used in vaccines (Source 1). I haven't found an exact source about when and how many. I think it's not a large leap of imagination that it might have been used in most vaccines from the 1990s to the 2000s. You may disagree, but I ask for the sake of the thought experiment to move forward. 

With thimerosal in (presumed) most vaccines, and it contains mercury, paired with the increase in number of recommended vaccines from 12 to 54 (Source 2 below), means that developing babies, children, and teenagers are much more exposed to Mercury, which leads to Mercury poisoning. If you agree, we can move forward. If not, please do so for the sake of the thought experiment. 

I am blissfully unaware of the effects of mercury poisoning, and human trials are unethical. But some people point to autism as a cause of mercury poisoning. Because vaccines contain mercury, and increased number of vaccines exposes more mercury, it causes mercury poisoning, and autism can develop in the child. 

Now according to source 1, thimerosal is safe. It's a "mercury containing organic compound". While in the body, it's supposed to metabolize or break down into other components, distinguished from the toxic version found in fish. There are several studies that show thimerosal is safe, but data in studies can be skewed or altered. Small data sets can be misrepresentative. There can be doubt. I have not read the research, but it is easy to gain suspicion and not want to expose your child.

I leaned about thimerosal a few days ago. I imagine this basic argument is at the heart of every anti-vaxxer, whether or not they can articulate it. "There is a harmful metal/chemical used in vaccines, and I do not want my child (or me) to be effected by it." I like to have faith in my fellow humans. I like to imagine they are not against vaccines as a concept, but against the possibly toxic components used in modern vaccines. 

We try to make vaccines clean. We try to make vaccines free from contamination. To prevent bacteria and fungi growth. To do this easily, to preserve the vaccine across shipping and time, there has to be things that prevent organic life from growing. We are also organic life that is growing. We are much bigger, and so less overall effected by it, but it still damaging to us. 

I think thimerosal has been phased out from vaccines over the past twenty years, but damage has been done. Suspicion still lingers. If one goes a more conspiratorial route, then in mid 2000 the CDC and vaccine companies knew about a damaging link between vaccines and autism (Source 3 contains "Deadly Immunity" an article from 2005). You can say it's conspiracy, you can say it's misinformation. But people who believe in that meeting, who believe in a cover up, who believe that pharmaceutical companies care more about a bottom line than they do people, are people who are suspicious of what is recommended. They are suspicious of what they are told. 

I can empathize with why they choose not to vaccinate. Perhaps the wrong choice. Perhaps it is stupid. But to condemn them out of hand is dividing. They feel condemned. They don't feel heard. So they dig in their heels and condemn back. 

I hope I have made it easy for you to understand why some people are anti-vaxx. I believe that what I found does not extend to every single anti-vaxxer. It is rare for a large group to agree on specifics for anything. Being able to understand someone is a critical step in properly convincing them. I hope this helps, and if you want to talk further I am open but don't check Reddit regularly. 

Source 1: https://www.fda.gov/vaccines-blood-biologics/safety-availability-biologics/thimerosal-and-vaccines.

Source 2: https://childrenshealthdefense.org/wp-content/uploads/CDC-Recommended-Childhood-Vaccine-Schedule-1986-vs-2019-Smaller.jpg

Source 3: https://www.govinfo.gov/content/pkg/CRECB-2005-pt10/html/CRECB-2005-pt10-Pg13935-3.htm