Where I come from it's just another fun family activity - but then if you've seen the Jeremy Kyle lineup around of any local areas where everyone is everyone's cousin, you'd know this cesspit of a town brings down the average IQ of the planet and sets the human race back a few millennia.
Apart from it being against our nature due to the declining genetic diversity and birth defects that it would bring about, there isn't really an actual moral reason, you are correct. But it is against our nature for that reason, so it is objectionable to us and isn't something I would ever have any desire to do.
Some cultures have done it for some reason - I think it was Ramesses III who I read recently married his own daughter? And according to the author, this was nothing unusual for ancient Egypt.