My off the cuff theory is that dancing is deeply tied to localized culture (often ethnic culture). Dancing was a major part of community life for ages, but with modernity came the fragmentation, even decimation, of localized community life. How many people work, shop, socialize, and go to church primarilly in their immediate community? How man people know their neighbors? How many people deeply engage in the social and civic life of their town? How many people receive an inheritance of community knowledge, which would include HOW to dance?
 
I'm guessing this began post industrial revolution when men began leaving the home for work. Cars, television, women entering the corporate workforce, and young people incentivised to move to major cities all likely accelerated the death of dancing as well. 

All this said, there are still subcultures across the US where people still get together to dance. I've been in some. Lindy and swing communities, churches that have balls and dancing functions where singles can meet, etc.