How does an alcoholic quit drinking if their partner drinks and doesn't want to quit?

You don’t. You can talk to him/her, tell them what you think, tell them you’re worried or you’re fed up or offer them help. These things may contribute to their journey toward realizing the hopelessness of their behavior.

Hi,
There is no definite answer actually. I would rather recommend to read how to quit drinking without aa http://addictionresource.com/alcohol/treatment/how-to-quit-drinking/ first of all and rate your chances. You see, it should be a decision that both should make. I used to quit drinking because of my husband and should say it was uneasy.