Its effectiveness at preventing the person who receives it from dying doesn't prove it also substantially reduces the probability of transmission, which is what the parent is talking about.
It beggars belief to imagine that your body is both more adept at fighting it and also somehow just as good at transmitting it.
COVID-19 Cases, Hospitalizations, and Deaths by Vaccination Status February 02, 2022
https://www.doh.wa.gov/Portals/1/Documents/1600/coronavirus/...
Summary
Unvaccinated 12-34 year-olds in Washington are
• 3 times more likely to get COVID-19 compared with fully vaccinated 12-34 year-olds.
• 5 times more likely to be hospitalized with COVID-19 compared with fully vaccinated 12-34 year- olds.
Unvaccinated 35-64 year-olds are
• 4 times more likely to get COVID-19 compared with fully vaccinated 35-64 year-olds.
• 7 times more likely to be hospitalized with COVID-19 compared with fully vaccinated 35-64 year- olds.
Unvaccinated 65+ year-olds are
• 5 times more likely to get COVID-19 compared with fully vaccinated 65+ year-olds.
• 8 times more likely to be hospitalized with COVID-19 compared with fully vaccinated 65+ year-olds.
• 9 times more likely to die of COVID-19 compared with fully vaccinated 65+ year-olds.
This can mean that the risk of hospitalization goes from 0.01% to 0.05%, which isn't something most people would care about. With statistics like that we need absolute numbers, not relative. Your post is basically an example of "how to scare people with meaningless stats".