What was explained?
The understanding of the effects of vaccinating kid #1 isn't all about kid #1 being immune to the infection. Instead it is that kid #1 is x% less susceptible to contracting the infection if exposed.
So you might wonder, how could Small Pox be much extinct if the vaccine is only about 95% effective, and how have we wiped out an enormous number of diseases that caused immense suffering in the 20th century using vaccines that were not 100% effective in protecting the vaccinated from infection on an individual level?
The lesson is that common sense can be a terrible guide for even the roughest approximations of the dynamics of a system. Dispersion models explain the limits to how far water will trickle down through soil or the conditions under which wild fires will burn themselves out. The models for infectious diseases involve variables for the likelihood of transmission, mortality rates, how long you're contagious until you show symptoms, the percentage of population that is susceptible etc.
While even common sense will tell you that the best way to avoid a disease is to avoid contact, it might not tell you that vaccinating populations is largely about reducing exposure. Assume our hypothetical situation has kids one through eight living on a street and they only play with their immediate neighbor. Then let's assume that the kids have a natural resistance of 20%, but 60% if they are vaccinated. If kid #8 has the disease, what is kid #1's risk of exposure if everyone is vaccinated vs no one is vaccinated?
(1-20%)^6 = 26%
(1-60%)^6 = 0.4%
I think those numbers are astonishing and beat the tar out of what common sense has to say. Of course more realistic models would show many more links between nodes as well as lower transmission rates, but differences of even a hundredth of a percent in a population of 320 million is 32 thousand people.
The conversation begins with: "The issue is not black and white — and laying the entire issue at the feet of non-vaccinated is blatant propaganda." If we're going to use extreme language, then it is "blatantly wrong" to say it is "blatant propaganda". The portion of people who defect from or cooperate with vaccination programs does matter. It isn't much of a problem if there is one Jenny McCarthy, but it becomes a problem if she advocates on behalf of defection to everyone else in her playgroup, or worse to other parents around the country.
While it is a good instinct to assume that issues aren't simple, it is tempting to see issues as having "two sides" and that the middle ground must be reasonable. I don't understand why newer/safer vaccines being less effective is being presented as a middle ground. If the "two sides" are not vaccinating and vaccinating, then this argument would not be in between the two, but instead it should be an argument that is more extreme than a mere decision to vaccinate. And yet, I think it serves to create uncertainty instead, and ultimately fewer vaccinations and lower resistance in the population.