I'm afraid the 'fallaciousness' is with your position!
The science of reduced transmissibility with vax is there. Just like the science of speeding down a suburban road at 100km/hour will definitely kill if you hit a pedestrian whereas at 50km an hour you are likely to have time to stop before impact and even if you do impact, the chance of death is much less.
Same with the vaccine. You are reducing, not eliminating, the chance of doing harm.
The extreme positions you are talking about are silly. It's about utilitarianism - with good policy promoting the greatest good for the greatest number or the least harms for the greatest number. The ethical choice is the utilitarian choice - not necessarily the nil risk choice. Maybe read up on 'game theory'. It may help.
