the "examples in their own families" you suggest? How about this explanation: "Members of the same family share common genetics and, in many cases, share similar environments--genetics and environment are what cause expressed traits (hair color, response to vaccines, height, etc.). Vaccines are only one of the environmental components they share, so how can these family members possibly know what causes whatever the problem is?"
The issue then, is the anti-vax crowd suggests that based on nothing more than uninformed, anecdotal evidence (and calling it evidence is generous), or worse-fraudulent research, we should decide public policy for vaccinations, which have been demonstrated repeatedly to be safe and which save many lives?
The next argument then, is that they haven't actually been demonstrated to be safe. Somehow, many, many scientists are colluding to dupe the world. BTW, scientists are people too, but apparently they're part of a massive coverup. You know the reason many of us go into science? <drum roll=""> To make a difference in the lives of people around us. So why, then, would scientists continually lie, for going on 100 years now, when one of their main motivations is to improve health? It most cases, science isn't about the money. I'm not a genius or brilliant, but I'm smart and I work really hard. I think that's generally the case for many in science. If money were my motivator (or the main motivation for other scientists) there are much easier ways to make lots of money.
So...there's no evidence vaccines are dangerous, and it's easy to continually call pharma evil, except that no one seems to remember that pharma is just a group of normal people, most of whom are probably pretty decent individuals</drum>