Yes there is a degree of false accusations and manipulation out there, and it is surely reprehensible. Not only for alleged sexual crimes against children, but those are the kind that society generally hates the most (and rightfully so).
I'm not so sure about this:
I think when we hear an accusation of this nature against an adult, it's only natural to be disgusted and want justice. That feeling (by an outsider) is not necessarily wrong, but it does have to be tempered by awareness of the POSSIBILITY that the accusation may be false. However, to impute the motive that "we need to believe we are better" is really not necessary.
If the crime actually occurred, of course we should be better than the perpetrator. But in most cases what you're seeing is a desire to see justice done on behalf of little children, the most helpless members of our society.