When people feel hurt, what they want is someone to validate their hurt, to say they understand. They tell the story of their hurt, in the hopes of getting affirmation.
Let's use some fictional names just for clarity, so I don't keep writing about "the hurt person" and "the person the hurt person is talking to." Let's say Cheryl is upset, feeling that Laura hurt her. Cheryl tells Laura why she is upset. She wants Laura to validate her hurt. But that's the last thing Laura wants to do. Laura feels that if she lets Cheryl's feelings be legitimate, that will be the equivalent of saying, "Yes, I did a bad thing. I am a jerk." It hurts Laura to feel like a jerk, so she wards off that possibility. She counterattacks, telling Cheryl she has no right to feel hurt.
So then Cheryl complains to Diane about how Laura hurt her. Diane may say, "You shouldn't let things bother you so much," or she may explain to Cheryl what Cheryl ought to say to Laura.
But if either Laura or Diane would just say something to Cheryl like, "I'm sorry. I can see why you're upset," it would do wonders to heal Cheryl's hurt.
Yes, this is something I feel strongly about personally, as I'm upset with people telling me what to do and how to feel. But it's also something I see all around me, hurt people taking out their stories, telling their stories over and over, in search of affirmation.
So, if someone is hurt, just listen and affirm their feelings. And, if someone is angry, the reason they are angry is probably because they are hurt, so if someone is angry, just listen and affirm their feelings.