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This is important and has a direct effect on your happiness, their happiness, and the success of the relationship. Don't waste time and energy trying indirect ways to “make her change.” It will just come across as manipulative and potentially cause resentment from your partner. Instead have a real, honest, and direct conversation about it.  Start by letting her know you need to talk. ”Alice, I think we really need to talk. There's been something that has really be bothering me.” Explain what the issue is for you; specific to your relationship. For example, if your partner is selfish or egotistical in conversations and making it about her, you could say, “I feel like when we talk, it isn't really equal. I love hearing about your day, but I'd really like for you to hear about my day too. When we talk, it feels really unevenly focused.” Ask for her input: “What do you think?” One of the great things you get to do in a relationship is to build each other up and watch each other grow. Help your partner grow by growing with him. Instead of focusing just on the person, try shift the focus to the relationship or the both of you working on the same thing.  You can try tasks like taking a relationship selfishness checklist test to increase your partner and your awareness of any selfishness in your relationship.   Humans are social creatures and tend to unconsciously adopt the goals of those close to us. Just like couples who learn a sport, how to cook, or a new language together, you can learn how to be less selfish and opinionated together. Make sure to celebrate and praise each other for positive changes you are making. The better you both feel about it, the more likely you are to continue to work towards the goal. This may be the most difficult part. If you are with an egotistic person, you may realize that changing these parts of  yourself can take time. Much like breaking a bad habit, you may have to be patient with your partner as she works on changing. Additionally, expect some backsliding into previous bad behaviors during this transition time and try not to be too hard on her. One way you can address this is to have a funny thing you do or say if you notice your partner slipping back into her selfish habits. Agree to an action or a phrase during your conversation. If you make it something you both find funny, it can take the pressure off of pointing it out.  The "Cut it out" hand motion Uncle Joey used in Full House. Playing a funny song such as Toby Keith's "I wanna talk about me." Saying, "Hold on, I haven't had enough coffee for this conversation yet." Pick something that is funny to you and your partner, like an inside joke that only you share. This may seem like a strange suggestion for an egotist, but often inflated egos and selfishness are rooted in low self-esteem or shame. Think of it as overcompensation. Your partner may have low self esteem causing him to exaggerate and inflate his outward display of what he thinks about himself. It turns out that he may be trying to convince himself of his greatness along with everyone else. Help him boost his self-esteem.  Avoid complaining about him or harshly criticizing him as it will only make him feel more threatened.  When  you are talking to him focus on his strengths and try to draw on the potential of those strengths. Compliment him not just for his looks, but for how he acts and what he does. The most difficult part about any interpersonal relationship is when you realize that you have almost zero power to change someone else. People can change, but that change has to come mainly from them. They have to want it. So if you are intent on a relationship with an egotistic person, your first step is to be real with yourself about the likelihood of the other person changing and begin to accept the selfish parts of her personality that you may not agree with. While you cannot change other people, you can help them to change. You can also control how you react to their egotism and the effect you let it have on your life.
Have a direct conversation about it. Urge the person to grow and mature. Be patient. Boost the person's self-esteem. Accept that the person may never change.