How can something be both traditional and iconoclastic?

I just read a phrase from Rick Santorum’s book, It Takes a Family, that reads, “and the greatest thorn in the liberals’ side, the iconoclastic traditional family”.

How can a family, or anything, be both traditional and iconoclastic at the same time? I thought iconoclasm was (other than the destruction of religious imagery) the attacking of tradition. Wordsmiths, help me out here.