If anything, this might undermine the argument by showing that certain vaccines are more associated with health problems than others. That could suggest something besides coincidence accounts for the health problems with these newer vaccines.

This questions the need for getting a vaccine. But this doesn’t help suggest that vaccines aren’t causing health problems.

This shows there’s no correlation between vaccines and higher rates of health problems in the period shortly after vaccinations. If vaccines really did cause the health problems, we’d expect an increase in the rate of health problems shortly after vaccination.

The comparative severity of health problems after a vaccine and problems the vaccine is designed to prevent is irrelevant. This issue relates to whether one should take the vaccine. But it doesn’t help suggest the vaccine doesn’t cause health problems.

If anything, this suggests that we should be open to a causal connection between vaccines and the health problems. But we’re trying to support the claim that vaccines are not likely to be the cause of the health problems people develop after vaccination.