Try extracting the main point from their pissed off reply and calmly acknowledge it and show appreciation for it. Even if you disagree, try finding the part you agree with. That way the person will feel heard and understood and will calm down.
Discussion
No, it is not my job to appease a grown man.
That's true and you do you. I found that with most people I agree on 80% or things and it always helped me first find the common ground before we get into the disagreement as it makes the disagreement discussion much more tangible and honestly easier.
There wasn't really an argument to be made in my statement in the first place. Only that often emotions get in the way that it is perceived as an attack.
It's like telling someone you love them. But because they're in a negative state of mind, no matter how sweet you may say it, it has no effect on them. It may even be perceived as an attack.