After reading through many reviews my analysis is slightly different . When Cooper let go of his ego and understandable anger towards Billie he was finally able to HEAL. When the divorce was close to closing, he made himself vulnerable by admitting to her that he missed her and the family being together and begged her to stay the night with him so the children can wake up and see them together. Billie declined. In a later episode he told her " you were the love of my life but I wasn't the love of yours" this was another step towards healing and letting go of the anger because the heart feels what it feels . Then the ending when he meetia another womann he wants to marry, and tells Billie " I can have two lovew of my life and not only is she the right woman for me but I am enough for her and that's the best feeling in the world" .