Why is Act Three, Scene Two the turning point of Macbeth?
One can make an argument for many scenes being turning points in Shakespeare's Macbeth: Lady Macbeth's shaming Macbeth into killing Duncan; Macbeth's killing of the grooms (a veering from his wife's plan which suggests his guilt to at least Macduff); Malcom's acceptance of Macduff as an ally, etc. Act 3:2 is not a scene that stands out as a turning point.
If you must answer a prompt emphasizing Act 3:2 as a turning point, however, the scene does demonstrate Macbeth's emergence as the person in charge, as the man, so to speak, who wears the pants in the family. Instead of relying on his wife to strategize and make plans, Macbeth has taken over the planning, as evident in this scene. Ideas of how to proceed are now his own. He makes the plans and carries them out without his wife's participation or consent. Act 3:2 reveals his plans to have Banquo assassinated. His wife is totally unaware of these plans. He has reversed the roles the two played in Act 1.
Of course, this is to Macbeth's detriment. He might have gotten away with killing Duncan if he had stuck to his wife's plan. Lady Macbeth is the planner of the family. Macbeth makes mistake after mistake once he takes over. Instead of relying on his wife, he decides what to do on his own. Worse, he also uses the witches as advisers. His poor decision making dooms him.
This is made concrete in Act 3:2. His wife is worried about their security. Macbeth tells her not to worry. He has taken care of the situation. He has ordered the assassination of Banquo. Of course, Banquo's assassination is just another coincidence that eventually leads Macbeth's lords to turn against him. And Fleance's escape ensures that Macbeth will leave no legacy of kings to rule Scotland.
In Act III scene ii Macbeth realises that the evil plan he and his wife hatched to dispatch Duncan has not been enough to secure him the throne -
We have scotch'd the snake, not kill'd it.
Macbeth in concerned that the witches told Banquo that the throne would pass to him, and Macbeth is plagued by this knowledge-
O, full of scorpions is my mind, dear wife!Thou know'st that Banquo and his Fleance lives.
We see Macbeth not only losing faith in himself but in the unity of his marriage bond. He no longer trusts Lady Macbeth with his plans-
Be innocent of the knowledge, dearest chuck,
Till thou applaud the deed.
Macbeth is to continue alone with his bloody quest to secure the throne for himself.