Yep, his moving in another direction and leading with his center are not possible at the same time. One of my teachers explains that to reach an offset position the leader initiates the movement with his body/center/whatever-just-not-the-arms, which initiates the follower's movement in the given direction. Then at some point the leader moves in another direction while his hands keep accompanying the follower to the original direction.
Yes, this is how I think of it as well.
You are describing several things that happen in sequence, not a single move (as clearly you know by the way you described it)
The leader DOES indicate
with a body lead the direction he wants the follower to go. AFTER she starts heading in that direction, he changes his own direction thus achieving a result of the two of them going opposite of each other (and to an observer, it probably looks simultaneous). But it is
not simultaneous. It is (as you describe) TWO separate movements by the leader... one is the lead for her, the other is his own movement.
The follower's job is to stay with him
unless he prevents it. In the case I think you are describing, he has effectively prevented her from staying with him through the timing of his switch. It comes too late for her to reverse her intention/ momentum. If timing isn't enough on it's own (and it often isn't except with advanced leaders) he will probably use his arms, not to
lead the move per se (because she is already moving as he wishes) but to
continue her moving that way by
preventing her from changing. And, as you say, allowing his arms to continue with her in the direction
he already indicated for her.
This type of move works best,
and is most comfortable for the follower, when she gets the clear lead from his body first. Too often the leader skips that part and uses only his arms to push her one way while he sends himself the other way. That's not so great.
So while someone can explain the correct method as "leading with his arms", I personally would make a distinction between using his arms to
prevent or follow her movement (that he has already indicated) vs using his arms to
initialize or propel her movement.
Obviously, there are times when this first type of use of the arms is required. (I'm thinking especially of those back sacadas where the guy rotates and turns his back to the follower to reach behind him for a sacada coming to her front. If she weren't prevented from following his chest, she wouldn't be in the right place.)
IMO, it is best to bring up these uses of the arms specifically in context rather than ever speak of leading with the arms. Far too often, beginners and even intermediate leaders (and leaders who have been doing tango for years but who still make fundamental mistakes) overuse their arms and try to lead or steer with the arms when it isn't necessary. For that reason, I usually say general things like "you don't need your arms to lead" or "You shouldn't lead with your arms". MOST of the time, it's true. The exceptions are rather specific instances, not general practice.