Been there!
What I learned in years of customer service work, was that no one NO ONE can resist being understood and their feelings/experience/expressions reflected respectfully. Sometimes the only thing you can do to defuse the situation is to put on your emotional tinfoil hat, and reflect:
"You seem very angry about that. If I understand what you are saying..."
"I can see how you would feel that way. You seem to be upset that..."
"Anyone might feel the same if they were in your shoes."
"I don't know if there is anything I can do to make it better, but..."
"Well it looks like there are two choices here. If you could tell me which you prefer..."
"I'm so sorry that you had to go through that..."
"From what you've told me, the problem is...."
"I will need to look into this/think about this/ask somebody/run screaming; would it be all right if I call you tomorrow when I know more... What would be the best time for you?"
Of course, that's customer service. I got all the hard cases, because I could talk ANYONE down. Its just business. Their problem isn't my problem, but my profession is to try to help them find a satisfactory resolution to their problem. So let's begin...
But in personal life, sometimes you are being abused. You always have the right to extricate yourself (FLEE) from an abusive situation, no excuses needed.
Oh, and sometimes, the person is just in need of a scapegoat, and you are the goat. When that happens, I will sometimes recognize what is going on, and just say "baaaaaaahhhhh" and start chewing on the furniture. It saves time arguing.