While it is widely accepted that vaccination is preferable to not vaccinating, would anyone like to give a shot at providing evidence in favor of not vaccinating? Anything goes.
Here's the thing. No one has been able to repeat the results seen in the discredited "vaccination is linked to autism" study that started this whole dangerous mess (I'm not even going to bother looking up the citation, I care that little about it). Scientists, including those funded by so-called "anti-vax" groups, have been trying for the past 15-20ish years, and they can't do it, because
there is no causative link between early-childhood vaccination and autism.
Your question is akin to asking us to advocate against Pasteur's germ theory of disease, or for the idea of phlogiston in chemistry, or against the theory of relativity in physics.
So, given that the scientific evidence is firmly pointing in one direction, why would we waste our time on this endeavor, especially when anti-vaxxers will cling to any sort of misquoted, out-of-context, partial evidence that they can find?
The only reason a child should not receive a vaccine at the scheduled time and in the recommended dose would be because she is severely allergic to one of the main components of the vaccine, or she has a significantly-depressed immune system, typically associated with cancer and other severe medical conditions. At such times, medical recommendations by the specialist treating the condition should be followed.