In Les Miserables, Victor Hugo says "Strong and bitter words indicate a weak cause."
That is usually true in negotiations. In my 25+ career as a transactional lawyer, I've been in thousands of contract negotiations. I've found that those who raise their voice or do most of the talking are overcompensating for a weak argument, weak negotiating position, or a low self-esteem.
In that situation, it's best not to respond in kind. That would just escalate things. Rather, it's better to handle it calmly. Try to tone down the tension by acknowledging their concerns.
"Speak softly but carry a big stick" is a proverb that goes along with this advice.