Other mistake: When Alice asks Dan to make her some tea (after he tells her about him and Anna), he walks into the kitchen for just a moment, and comes back to find her gone. He also doesn't see her as he runs downstairs and looks outside. She couldn't have quietly gone down the stairs and out of the building in the short moment that Dan was in the kitchen. If she had moved quickly, there should have been a lot noise from her footsteps.
Closer (2004)
Plot summary
Directed by: Mike Nichols
Starring: Julia Roberts, Jude Law, Natalie Portman, Clive Owen
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Answer: I think it was because of the offer that Larry made to Anna. He promised that if they had sex one more time, he would leave her alone and never contact her again. The fact that he was willing to give her freedom, is what made her choose him. Dan was more "needy" and pushy, which is hypocritical, because he left Alice based on her being needy.
Dan left Anna after confronting her about sleeping with Larry for the divorce papers. Anna begged Dan to not stop loving her, to not leave her. Looks like Dan could not stand Anna after she slept with Larry so she went back to Larry since she never turned in the divorce papers.
But after the incident, Dan went to Larry's office and begged him to "let" Anna return to him.