If someone says goodbye in an angry mood, it's essential to respond calmly and respectfully, even if their tone is negative. Here's an appropriate response:
"I'm sorry to see you leave feeling this way. If there's anything I did to upset you or if there's something on your mind, I'm here to listen and try to understand. Let's talk about it if you're willing. Take care."
By responding with understanding and openness, you demonstrate empathy and a willingness to address any issues that may have caused their anger. It's essential not to escalate the situation further by responding angrily or defensively. Instead, aim to defuse tension and maintain a respectful conversation if the other person is receptive to it. However, if the person continues to be confrontational or disrespectful, it might be best to disengage and give them space to cool down. Always prioritize your safety and well-being in such situations.