This is the CDC website. Sure seems like the vaccines mostly do prevent infection aside from a few breakout cases because they "are not 100% effective".
And the CDC's guidelines affect a heck of a lot, including whether your kid can go to school. If they don't prevent infection, why are they on the schedule? Shouldn't individuals be able to decide on their own if they aren't risking public health?
You raise good points about the CDC’s inclusion of the vaccine in the childhood schedule. However, that was not the point he was making about the tweet, and it seems you are misreading what the CDC writes about the vaccines.
It appears you would prefer a different wording than “not 100% effective at preventing infection”, how would you write it? Remember it does still appear to be somewhat effective against infection although we will obviously see millions of breakthrough infections.