Celimene does not respect Alceste, because she cheats on him and lies to him.
Celimene plays all of her suitors. Although Alceste tries to treat her with respect, but telling her the truth, she continues to lie to him. She considers him just one of many, and is more interested in keeping her place in society than in finding true love.
Celimene accuses Alceste of quarreling. He explains that her behavior with other men bothers him.
Then, do you hold me guilty be-
cause men love me? How can I help it if they
think me lovable? And when they take such
pleasant pains to see me, am I to take a stick
and drive them forth? (Act 1, Scene 2)
In the end, Alceste decides he is tired of playing her game. He loves Celimene, but he wants her to love him too. She has to be able to give up her influences on others, and their influence on her.