Don. Why does the man have to turn the body slightly anti-clockwise. Does this mean that he has to have his body facing one way while his feet are facing another way?

Dancefad,
The twisting of the body by the gent to the left is a 'throw-back' to the 50's. It was wrong then as it is now. On my many travels it is not unusual for me to see the gent do this having taken the Tango hold. Some gents have been told to do this and others have seen in being done and blindly copied it. It is also a fallacy that the Tango walk has to be curved to the left. The walk can also be danced without the curve. Hope that this helps you to understand.

To clarify, the character of tango is not ultimately curve, but rather movement diagonal to feet and body. This takes the form of alternating CBMP and side lead steps.

From the man's perspective, the left foot CBMP step is performed by tucking the right knee behind the left, which rotates the hips alone in an anti clockwise direction, without disturbing the top. The actual left foot step is taken moving towards his right hand, which is a diagonal across his body that we call CBMP. Next, without changing anything rotationally, and keeping his feet parallel, he takes a step with his right foot, continuing to move in the same direction. Because his right shoulder (or more obviously, his right hand) gets there first, we say that tango has right side lead. But we do not rotate the shoulders to put the right side in advance.

After two walks, one could keep moving in this direction for another two steps, alternating CBMP and side lead. More commonly, one will execute a bit of turn in place before commencing the next left foot step, but as Iluv2Dance says, this is optional. If pairs of walks are danced with a turn before each left foot step, a circle made of straight sided segments will be completed. A small amount of turn between the left foot and right foot steps may be tolerated, but this should be kept small as it tends to square the bodies to the feet, forcing the right foot step to be smaller than it could be if taken with a side lead. Allowing the shoulders to rotate anti-clockwise during the right foot step is highly suspicious.

Again, it's vitaly important to understand that the side lead is not achieved by rotating the shoulders anti-clockwise. Doing so would involve the very risky pulling of the left side away from the partner. The shoulders do not rotate, the path of progression is just at an angle to them, which means that the right shoulder (or more dramatically, the right hand) gets there first.