Tango the drink is an invention counting only a year or two of life, while tango the dance is an invention of the early 20th century - so it's quite clear where the saying 'it takes two to tango' comes from!
And as for a little background info, tango is indeed a very close-contact dance for two people, (usually) a man and a woman. The man leads the whole dance (even if somewhat less nowadays than in earlier times) and the woman has to 'read' the man's lead and follow properly. This communication between the dancing partners requires this close contact in order for the man's leading 'signals' to be clearly felt by his partner. The woman, in turn, has to respond properly and quickly enough to her partner's lead, so that the dance goes on smoothly, creating the beautiful image we see competent tango dancers achieve on the dancefloor!
Now I think it's clear why 'it takes two to tango'!