Just tell them to f*** off. That's all.
Or, change your mindset. Try to adopt their worldview. Understand that your customer is upset, and that a problem has to be solved. It doesn't matter if it's your fault or not. It doesn't matter if it's unfair or not. Just leave your ego on the side, and help your customers. They will feel important. A customer with such a feeling is a high LTV customer.
" I'm sorry. If I were you, I would be really upset. You're kind enough to not cancel your subscription. Let me change this, and everything will be ok."
" I'm sorry our app is down. We had some database issues. We're fixing them, and I can send you a text as soon as everything is fine. Is that ok ?"
" I'm sorry that you find our customer service is very bad. Could you explain me what you disliked, and what you'd like next time ? It will help us improve our service.
I wouldn't give them ideas!
In any case, I think what customers want when they're angry is for you to 1. accept responsibility, and 2. fix it as soon as possible.
We entrepreneurs are supposed to be problem solvers.
Own the problem, solve it, and we're rewarded for it.
Literally our raison d'etre.