The Pathfinder rules here aren't very clear, and part of that is because of the shift over from 3.5. However, Paizo's Official FAQ has some relevant information:
Acrobatics allows you to make checks to move through the threatened area of foes without provoking attacks of opportunity. You must make a check the moment you attempt to leave a square threatened by an enemy, but only once per foe. The DC (which is based of the Combat Maneuver Defense of each foe), increases by +2 for each foe after the first in one round. The DC also increases by +5 if you attempt to move through a foe. In the case of moving out of the threatened square of two foes at the same time, the moving character decides which check to make first.
For example, a rogue is flanked by a meek goblin and a terrifying antipaladin. The rogue move away from both of them, provoking an attack of opportunity from both, but uses Acrobatics to attempt to negate them. She must move at half speed while threatened by these foes and can choose which to check against first. If she fails a check, she provokes an attack of opportunity from that foe. If she makes it, she does not provoke from moving through that foe's threatened space this turn.
And so, even though it does make sense to decide that the "through" language must be purposeful and that it means something different from "leaving a square", that's actually not the case, and the Offical FAQ goes so far as to use an example where a rogue starts her turn already flanked by two enemies.