I spent SO MUCH TIME during my pediatrics clinical rotation explaining vaccines to new parents. In some cases, I sat there for a literal hour and debunked myths and conspiracy theories in order to get the parents to consider maybe doing a delayed vaccination schedule. I'm a medical student, so my time is basically worthless and I viewed this as a good use of it, but it was so incredibly frustrating to have to do over and over.

For other folks who know anti-vax parents (new or not), here's the best line of argument I came up with:

Vaccines have been around for a very long time now, and the only changes we've made to them recently is to make them better and safer. The preservatives in them like the mercury compound are perfectly safe, but we've still worked hard to improve the manufacturing process to minimize the need for those preservatives and make the vaccines as pure as possible.

Vaccines are made of little fragments of the virus or bacteria, or a modified, significantly weaker version of the pathogen to give your child's immune system a chance to see it before the real thing shows up. It's like giving your child's immune system a wanted poster or a punching bag to practice on because it has to make special tools to fight each different pathogen.

The reason we load kids up with so many vaccines in the first year or two of life is because their immune systems are still growing and it's an optimal time to introduce things for it to prepare for, and we want to give them some protection of their own before the antibodies from mom run out around 6 to 12 months of life.

We have decades of data showing that vaccines are safe and effective, and the complications and side effects are so minor compared to the problems that can come from the disease. And it's usually around 1000:1 ratio of complications from the disease versus complications from the vaccine, and the vaccine complications are almost always less severe than the complications from the disease.

If you refuse vaccination for your child for reasons besides an anaphylactic allergy to the ingredients, you are gambling your child's life with most of these diseases, and it would have been an entirely preventable death. Vaccines are very hard to make and we have prioritized making vaccines for the diseases that kill children. We don't bother making vaccines for things that are just a nuisance, so the vaccines we have exist for very good reasons. For the most famous example, measles has about 5 different ways it can kill your child that are impossible to treat or prevent once they have it, and many ways to cause permanent damage. The known and most common side effects of the measles vaccine are pretty mild and can be easily treated with medications we have available.

Edit: Fuck it. I've decided that I'm going to use some of my copious (/s) free time writing a children's and parents' book about vaccine safety with this argument. I will self publish if I have to and give it out in family medicine and pediatric clinics if it kills me.