You are technically correct (everything is harmful, and vaccine application is probably associated with some amount of micromorts — but so is, say, getting up from the bed). However, vaccines are very safe (safer than many everyday activities), and negate much more micromorts. Thus, I believe that your technically correct appeal doesn't contribute anything useful to this particular discussion.
Vaccines are harmful; it's just that the positive effects vastly shadow the negative effects in the general case.