This is a myth. The original reason babies are not vaccinated is that they are supposed to be already protected by maternal antibodies, and therefore the vaccine won't work.

Nowadays there is a new problem of people spreading the myth that vaccination is known to be dangerous to infants, so it is not politically acceptable to lower the vaccination age. This is even though we know the maternal antibodies of vaccinated mothers wear out sooner than those of earlier generations (who generated them in response to a full on infection).

I explained this a number of times in an earlier thread: https://news.ycombinator.com/item?id=13655795

For example here: https://news.ycombinator.com/item?id=13656462