he wishes one of his daughters was a son

We can make it happen. We have the technology.

he’s always cajoling his wife into bearing him another child so he can get his matching set

I’ve heard this sentiment before. I’ve even heard of folks doing IVF just to guarantee gender.

But that tends to be a separate phenomena from the Gender Reveal Party, which is more about making a spectacle of the reveal than being invested in the outcome.