What is the essence of tango and the milonguero style of tango dancing that’s the basis for tango social dancing in Buenos Aires; what differentiates it from other styles of tango.
Milonguero naturally incorporate these elements into their dance without thinking about them or perhaps even realizing what they are doing. They may be unable to explain these secrets to others, since they are a natural part of the dancer’s expression that they may been using for thirty years, fifty years, or even longer. Their partners marvel at the subtle differences — though these differences are difficult to explain and difficult for others to observe and understand.
ENTREGA
Total surrender to the embrace and the music
Entrega, as described by one woman to another …
The Holy Grail of Tango is entrega… and entrega is a trinity. It has three parts: man, woman, and music. To attain it, a man and a woman must both have an informed passion for the music. They must understand and feel deeply together, and they must both be willing to put all the meat on the fire—to surrender themselves with no self-consciousness and no vanity. Rick McGerry
LA MARCA
The follow waits for the invitation, the suggestion; the lead shows her the way.
ABRAZO
Cadence, Posture and Steps (Walking) are All that Matter
But in tango the key is to know which things are worth such close scrutiny. Dancers who spend too much time analyzing patterns and “moves” tend to develop a mechanical style that’s easy to spot. And if you dance that way in Buenos Aires clubs, you’ll quickly join the ranks of the invisible people. For me, there are only three things in tango that are worth putting under a microscope: Cadence, Posture, and Step. You can’t examine them too closely, and you can’t practice them too much.
~Rick McGarrey and his masterful website TangoandChaos.org
tango chose me 
I don’t know what those teachers are rreerfing to, but Ruben and I dance and teach what we think of as traditional tango in BsAs, and this is it. Of course everyone dances his/her own way, and we don’t dance like this, but it is the same style of social tango.To us, traditional tango is defined as inspired by the music, is improvised, is all about the connection,embrace, elegance, and sensuality.But perhaps those teachers have another definition.