There is a ‘firm’ embrace, and then there is Constriction within the embrace. Constriction in this definition refers to bodily compression usually with the forearms, biceps, and/or hands creating pressure and compression against, and around your partner’s body (at the bra line or at about the 7th/8th Thoracic) thereby (so the thinking goes) constraining their motion. This is done, not out of malice, but (for example) to stop or to contain someone's motion, or to stabilize one's motion. In short, you would constrict your embrace (from a leading perspective) to stop motion for the Follower. However the Follower can initiate Constriction as well, to ‘hold on tight’ to their Lead. This is ‘Constriction’ (and really ‘Restriction’).
From time to time you will run across dancers that state, rather vociferously, that you must be very firm in your embrace (lead or follow) which is all done in the service so that you can ‘feel’ your partner. At the same time there is an emphatic statement that they can’t dance or relax into the embrace unless that firmness is present, constantly. While there’s nothing wrong with this way of dancing except that it was true...once, that people used to dance this way, it’s not necessarily true any longer as the only way to dance. It has fallen out of favor to a larger degree.
What you may fail to realize is that this way of thinking, and dancing, is more than a little restrictive to the modern Tango dancer. It doesn't allow for the free range of motion that is required with how much physiological rotation that the dance has become over the last 20 to 30 years (thanks Gustavo!). Further still the dance has changed since the 30’s and 40’s when this idea was conceived. It was a very different time. Furthermore when this idea of dancing came into being as a method to dance, it was a way to ‘control’ the Follower. It was telling them where to go, and how to get there. Think about the time period: The role of women in society was ‘diminished’, and therefore chattel by all rights and means. A woman’s role was to do what she was told. Period. Women's rights ? Ha! Put that all together and the idea of constriction is incompatible with today's modern version of tango.
At one point in time, there was logical reasoning involved: Tango without that constriction requires too much work on the part of the dancer to ‘listen’ to your partner. That you must really focus, on what your partner is doing. And that focus takes away the ‘dancing’ part. So it is easier to constrict the embrace and tell/be told what and where to go and how to do and how far or how much less to engage by employing Constriction. Further still without the constriction of the embrace, there’s too much, too many variables that can go wrong, that you can’t be certain what was intended unless there is physiological pressure, arm tension, muscled force, engaged resistance, etc.
The Tango Topics Opinion is that this line of reasoning is a fallacy, and absolute laziness on the part dancer. It is uninformed thinking and dancing. Truthfully in today's modern version of Tango, one must develop a kinesthetic Hyper-Awareness of pressures, positions, and proprioception in order to raise your level of dance to pinpoint accuracy without using force, tension, resistance, compression, pressure, rigidity, stiffness, constriction, or restriction in any way, shape, or form. Rightfully this way of dancing is called Intention Based Dancing