If people don't want to give anti-vaxxers ammunition, then we should avoid the subtle falsehoods in the claims. You can't claim that the vaccine "prevents infection" because technically it doesn't. It is "X% effective to prevent serious infection." That's just how the science behind vaccines works.
Personally, I'm not too worried about covid because based on my demographics and health, the statistics say I have a very low chance of serious case or death (less than 0.5%). However, I was even less worried about taking the vaccine because the data on the reported adverse side effects are WAAAY lower than my chances of getting a serious case of covid. Easy comparison and decision for me.