Put it in a note.

she understood your explanation... but she made her choice and could not under any circumstance admit you were right. either see the fight through until you win or know when to surrender early... middle ground with parents at least for me has always been the worst loss even at 27 living on my own. the fight is either worth walking away from or taking it to the bitter victory, otherwise Its all over FBI, and I hear about at every gathering... the point is, win or walk away before any escalation happens

OP, is mom by chance either partially deaf or perhaps she does not speak the language you used well? If that’s the case then the problem is a bit more understandable. In that case try communicating with her again to explain what happened when she’s had time to cool down. If Mom is showing signs of dementia (Google it), there is a bigger long term problem that needs to be faced with the rest of the family before it gets worse. And sadly nobody is going to be happy about that discussion, least of all Mom. Bring the issue up to her doctor if this is the case. On the other hand if Mom is simply an over-reacting idiot who won’t listen to reason, you are going to either have to learn how to handle Mom better or move out when that’s possible. It’s usually easier to avoid escalating an argument than to patch things up later. But if Mom has a habit of this kind of behavior and it’s not due to the two things I mentioned above, then she may be used to “winning arguments” purely by volume and bad behavior. In that case you need to pick your battles to those things that are worth it and be prepared to simply walk out if necessary.