I've re-read Fruits Basket around 3 times, and on this third reading I noticed something for the first time. Akito and Shigure are the cause of just about every event in this manga. Akito's personality began to take a turn for the worse after Shigure begins to emotionally detach himself. He starts to emotionally detach himself because he wants Akito as a women, not as his God. Everything Akito does in this manga (outside of her bets with her Mother) she does to try and bring Shigure back to her. She mentions later in the manga how Shigure was the one she could never catch, she could never truly control him like she could the others.
Once I started realizing this I noticed how many games they play with each other throughout the story. Half of the characters are just pons in this intricate game of Cat and Mouse; where both Akito and Shigure are both the cat and the mouse. If neither of these characters existed, then almost none of the events in Furuba would've unfolded so chaotically.