But the act is "dragging the opponent into your space". My opponent is not "dragging the opponent into your space". He's leaving a threatened square.
Remember footnote 1 to Table 8-2:
Regardless of the action, if you move out of a threatened square, you usually provoke an attack of opportunity. This column indicates whether the action itself, not moving, provokes an attack of opportunity.
It's perfectly possible for an action not to provoke an AoO, yet movement out of a threatened square resulting from that action to provoke an AoO.