I suppose reasonable debate means ducking a simple question:

"How can marriage be an incentive to stop the promiscuity, when only a tiny minority want it?"

Let's suppose your "tiny minority" statistic is factual (you need to show that it is if you want anyone to believe it, but let's just suppose...)

Why would you deny marriage to this tiny minority? Wouldn't this help solve the health crisis you are so worried about...even just a little bit?