The compelling reason is that rights are being denied to a group of people that:
#1 it is not illegal to be gay
#2 it is not illegal to be in a gay relationship between consenting adults (non family)
#3 It is not illegal for gays to raise children
Therefore it shouldn't be illegal for them to marry.
Now if you want to go down the slippery slope on polygamy, I have no problem with that either. Polygamy is more of an administrative problem than anything else.
You, however, have not presented a compelling reason to disallow gays to marry.