The history of Tango is fascinating and complex. The evolution of the dance has profound implications for the way we dance today, and Tango music has become one of the great World Music genres.
The great dancers, those who were genuinely part of the living culture of Tango, have tended not to have academic backgrounds, while the academics in Argentina have tended to neglect the dance, concentrating instead on the music.
There is a cliché that Tango was born in the brothels of Buenos Aires. However, a more likely explanation is that the brothels were where people of the upper and middle classes first encountered it. Brothels were major places of entertainment for the working classes.
A shortage of women in the population also meant a shortage of women to work in the brothels. With many potential clients and few working women, the consequence was that there would be queues in the brothels as men waited for the women to become available.
Brothel owners in Buenos Aires would employ Tango musicians. In both cities, these musicians were playing the music of the poor, and brothels were amongst the very few places in that section of society that could afford to employ professional musicians.
The idea that it was the prostitutes in the brothels that danced with the men while they waited is an appealing one, but doesn't make logical sense. The point was that the men were waiting because the women were otherwise occupied. Obviously the brothel's income would be maximised by keeping the girls busy at their primary occupation, so certainly at peak periods where the brothel was busiest there would not be women available for dancing.
However, if there was music then it seems to me to be a pretty safe bet that the men would have used the opportunity to practice their dancing together.