Emotions are complex. Under the anger or accusations (the HARD emotions), there are more vulnerable emotions, like fear, anxiety, embarrassment, hurt (the SOFT emotions). Sometimes our strongest (soft) emotions hide under other (hard) emotions because they represent our deepest needs and fears, and it can be scary to express them. And so we may use secondary harder emotions (like anger) to mask them.
Try to look for the soft emotions under the hard ones, and respond to that. Bringing it back to the soft emotions can soften an argument and make it easier to resolve. It’s not easy, but it addresses the real problem.
Additionally, it is working with those soft emotions, those feelings of vulnerability, that build intimacy and closeness.
With care and concern, you might say, “I am getting a sense that there is something deeper here, under what you just said (under that anger, accusation). Is it that you are afraid of something? What is it?” (And of course, validate and respect those softer emotions. Never minimize or belittle those.)