I snapped at something she said and she snapped back. I responded that if I got her intentions wrong and she knew it why did she snap back at me instead of trying to resolve it or explain it right there. She argued that I just need to change how I respond. Sounds similiar to what you went through.
In your case you could have kept saying you didnt need help when he tried and he could have just stopped trying. I am guessing both are driven in natural responses.