The plague hit in 2017. A variation of the flu that achieved near-universal communicability, nearly everyone on the planet had it at some point - at the time we just thanks our respective gods and stars that the symptoms were only fatal to those whose immune systems were already compromised in some fashion so the actual fatality rate was very low.
Then the babies stopped coming.
Testing discovered that while the "Man Flu" killed very few it did greatly hinder male fertility. In 2018, most of the world's men didn't even have sex drives - let alone get erections. When all was said and done only about 2% of the world's men could still get a woman pregnant.
So something drastic was done. The remaining fertile men began forming Breeder's Union to protect their legal rights. Now the Breeder's Unions are legally recognized in the vast majority of the world's countries. Membership given to the few men left that still test as fertile and from that all sorts of arrangements can be made.
Basically a less extreme version of my GPBL RPs, we can arrange what all of this can mean. Perhaps Union members make deals with companies for mates, or the Union Chapter houses can be visited like fertility clinics. Hijinks Ensue, clearly.