I don't wish to speak for anyone else but surely it is sensible to avoid taking drugs unnecessarily? Particularly for children.
Vaccines are drugs, they are pharmaceutical products, and they are administered by injection.
I think it is worrying that we have reached a level of complacency towards these drugs that we are willing to give them to healthy children when they potentially do not offer benefit to those children.
Of course where one stands on this comes down to how you feel about drug/medicine/vaccine safety. If you think the safety, testing, surveillance and quality of pharmaceutical development and production is beyond reproach then an unnecessary vaccine won't worry you.
For the more cautious amongst us, we prefer not to expose our children to substances that will not do them any good (in the case of immunity already being present) and which have the potential to do harm.
And I think the thing with vaccine safety is that while most children seem to react ok, when a child does suffer a bad reaction, the consequences can be devastating. So IMO it just seems humane, sensible, responsible and common sense to avoid unnecessary vaccines.