Moment arm (pun intended). Connecting the bodies with the help of the arm helps you make a semi-rigid body from two independent bodies in a way that is hard without the help of the arms.
Unless you happen to have a prehensile torso (well, actually, come to think of it, I have a prehensile torso with prehensile appendages conveniently situated outside to maximalise the moment arm. I think my wife refers to them as "arms").
You don't always need all the arms and sometimes one partner doesn't even need any arms (in close embrace with one follower arm wrapped completely over the shoulder to the other side of the back, the leader can actually dance with both arms dropped and passive). But I have yet to see an embrace that works with *no* arms, unless ones on which the eyes are used to get cues (and I don't like these at all). But then, I'm not ready to enter the New Age, so I can't feel all those vibrations emanating from my dance partner

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