Parents and their children and siblings already have that next of kin relationship. Therefore, they are not eligible for a marriage license.
It's just that simple. Why haven't Conservatives realized this for themselves?
There's nothing sacred or written that marriage is to merely establish a "next of kin" relationship. It is a sacred bond between two people in love, expressed to others. One legal aspect though of marrying a child is that spouses automatically inherit first in many states, then if they die, the children MIGHT have a claim to what's left of the estate. If you wanted to be sure your child was the sole heir of your estate, marrying them would make them your legal spouse: and therefore automatically entitled to all your estate.
I like how the cult of LGBT is suddenly so prude and old fashioned when it comes to
"the traditional meaning of marriage...therefore..." 
But hypocrites are so beautiful in their purest form, no?