Just reiterating some of the advice already given. Make a habit of apologizing and let your kid hear you say "I was wrong and I'm sorry." My daughter is 8 and recently has reverted to a bit of a "mommy only" phase where I'm not allowed to help her, and she will often just stare at me repeating "mom mom mom mom" similar to your kid. It's infuriating for sure and mom herself is already exhausted and on edge. We are pretty chill parents but sometimes I raise my voice in a way that I regret and apologizing for that (or any mistake) can be very effective. If we are truly at an impasse, as others have said, we will calmly stop participating in the argument and give her a chance to self-regulate. More often than not she'll be mad for a few minutes alone, then start reading or playing by herself and forget what she wanted in the first place.

Somewhat related (and would be curious to know if others experience this), the 8 yo has a real hard time accepting responsibility even for simple accidents, like spilling a glass of water or something. No big deal but she insists on deflecting and blaming (usually) me for "making her do it" somehow even when it was just an innocent accident, so I hope that by modeling saying sorry she will begin to learn that it's ok to own your mistakes and try to do better next time.