Responsible Anger Management

I have a question about this episode Esther Perel: How to Find, Build & Maintain Healthy Romantic Relationships and this Conflict to Connection. My partner doesn't seem to think it's healthy or productive to allow the hurt partner to have their "moment in the spotlight" while discussing that person's hurt or concern. For example, if I come to him with something I'm sad about, he responds with comments about how I do that too, or how I do XYZ and it hurts him, or else he will bring up how he hasn't healed from the dinner with the ex. He also seems to consider every disagreement or discussion about relationship issues that need a compromise as a "fight," and he often gets very angry, starts yelling, and tells me to leave the room. What should I do in this situation?