Brian wants more from the relationship than his allotted two hours, and he makes a serious play for Arielle by buying her a ring and asking for a deeper commitment. She initially acquiesces, which prompts her husband to pay Brian a furious visit. But when Brian shows up at their favorite hotel spot, Arielle has left him a note that graciously lets him down in favor of keeping her commitment to her husband and children. She also requests that they never see each other again. A few years later, Brian is a successful author who’s published a book about the affair (called The Mermaid) and now has a wife and child of his own. His family happens to run into Arielle and her family at the Guggenheim, and while everyone exchanges pleasantries, Arielle furtively removes her glove and reveals to Brian that she kept his ring on her finger. Perhaps she regrets making the decision she made, or perhaps she just keeps a place for him in her heart.
The third option—which the film doesn’t suggest, but which is suggested by the story—is Occam’s razor: The two of them had an agreement, he violated the terms of that agreement, and she voided the deal. There was never any indication that Arielle was unhappy in her marriage, or unhappy with the 5-to-7 stricture of her affair with Brian. For him to buy a ring and actively attempt to break up her marriage crosses the line and puts her in a terrible spot, especially if her feelings for him are legitimately strong. He forces her into a choice she never wanted to have to make and she makes it. That’s on him.