How to deal with someone who is committed to misunderstanding you:

You're caught in their emotional vortex.
Your only role is to: not take the emotional bait.
It's to stand regulated in your own emotional energy.
1. You're not on trial: you don't need to prove your intentions or motives just because someone claims to know them.
Say: "I understand that's your perspective." nothing more.
Say: "Ok, I understand the way you see it."
Say: "I'm not available to have that conversation." Never argue about someone outside the situation.
If they get dysregulated, loud, or overbearing stay calm. Be neutral. Say much less than you think you should and let them do all the talking.
Explanations are asking them for permission. They'll use explanations to build more and more conflict or tension.
Everyone is entitled to their own perspective.
You just don't need to take it as your own.
You're not trying to prove a point, you're trying to protect your nervous system. At any time you can calmly end the conversation and show them you don't need their validation.