Cousin marriage
So, the main argument against cousin marriages is that it increases the likelihood of genetic defects occurring in children of such marriages. The classic example of this is the occurrence of haemophilia (and some other conditions) in the royal families of Europe. The repeated marriages between close relatives increased the chance of recessive genes arriving on both chromosomes of a pair, so causing defects to appear. Of course, pre-scientific societies would not have known this. However, they would have seen the results of continual close marriages, such as the brother-sister matings in the Ancient Egyptian royal lines.