Precisely.
Society recognizes marriage between a man and woman because only that coupling can perpetuate society.
What exactly can society derive from same sex marriage? Nothing, same sex marriage can only take from society because those relationships will never give society back a future generation. Even if a marriage between a man and a woman result in no children there is at least to society a possibility, no matter how small, children could result from such a union.
For same sex relationships society recognizes the possibility for that union to create children is simply impossible.