Salam, the Prophet said there is reward to leave an arguement even if you are in the right, so when My mother tried to argue with me about giving food to the cat (that would otherwise go in the trash). It was v late at night and she was increasingly getting angry and I repeatedly said I will not argue and when she did not stop I went outside until she stopped yelling. Now she is not talking to me. This behaviour, especially in Ramadan is upsetting. Did I act wrongly by walking outside?
Alaikumassalam wa rahmatullah,
Not arguing does not mean stopping in the middle of the argument while holding onto your own position. The other person will still feel like you are arguing, since you are not ending the argument just pausing it, and they can feel insulted by that. Leaving an argument means to put a quick ending to it in a polite way, and this usually means giving in to the other person’s position. The point is to sacrifice your own desire to win the argument and make the other person feel like they have won. If they do not feel like that, then the argument has not ended.
So the right way to have dealt with your mother in the situation you mentioned would have been to either let her win the argument or reach a compromise that satisfied her.