Hard data and facts agree vaccination can be harmful in extremely rare cases. Anti-vaxxers would likely argue against the exact definition of "extremely rare". Only the uninformed defend vaccines as universally good. The scientific consensus is that the benefits for the population as a whole far outweigh the negatives for individual cases.

Vaccinating everyone protects people with weak immune systems, and vaccination has managed to eradicate certain diseases in the first world. Some of these diseases are making a comeback due to increasing immigration from unvaccinated populations as well as homegrown anti-vaxxers movement.

On the flipside, most vaccines come with a ~20% chance to cause local pain (and we are increasingly learning pain in the formative years can have long-term consequences), and a ~5% chance to cause a fever. Sometimes the consequences can be more dreadful: the MMR vaccine is estimated to have a one in a million chance of causing body encephalitis, which has a very high death rate.

It's a cold calculation. Vaccination kills less people than no vaccination, but it does kill people who might live otherwise. This makes sense both at the population scale and even as a parent, but statistics mean nothing on the individual level when your kid is the unlucky one.