Being vaccinated does not prevent you from carrying and/or spreading a virus. It does not create some super secret aura that the virus cannot penetrate.
I never said that herd immunity protects by magically conferring immunity to unvaccinated people. It works by having enough people vaccinated to break the chain of transmission. If you cannot be vaccinated for some reason, but everyone around you is vaccinated, you won't get the disease because no one around you will get the disease.
And you did not read my post correctly. I said the vaccinated person can still transmit the pathogen to another. A vaccine does not prevent transmission, therefore how can vaccination break the chain of transmission?
I noticed in previous posts that you are a medical researcher. If so, then please humor me and explain what you mean by "getting the disease"? I refuse to believe you do not know how a vaccine works. You inject a known antigen to stimulate the production of antibody to that antigen. Then if said antigen is inhaled, ingested or otherwise introduced the antibodies attack the antigen and the vaccinated remains unsymptomatic. The vaccine does not prevent the pathogen from entering the body or being carried in the nose, saliva, or even on the hands, etc. Those pathogens, while unable to wreak havoc on the vaccinated, can still be transmitted to others who are or are not similarly protected.
The herd immunity theory implies the effectiveness of the vaccine improves with the number who are vaccinated, as if the vaccine destroys the pathogen so that the more people vaccinated the fewer pathogens will exist. It simply doesn't work that way.
Vaccinate your children if you believe it's the right thing to do - but please do not attempt to guilt anyone else into following your example using false premises such as herd immunity.