Grammar Grumps

When the six-year-old brother comes in from playing croquet to ask for--what was it, the yellow mallet?--because "Devrah and me" need it, the grammar grumps (ages 11 and 48) stall communication when they keep keep correcting "Devrah and I . . ." and the six-year-old restarts "Devrah and me . . ." This back-and-forth repeats itself a few times with the little brother not choosing to take the hint ends with the 11 year old saying where to find what he wanted.  The little brother concludes, "Don't fight over that, because that doesn't sound good."

What's at stake here?  Why did the grammar grumps waste the little boy's time?   Or did they waste his time? Why did they break down communication by smartly attempting to teach the little boy?  Why does me as a subject feel and sound right to us?  And are these rhetorical questions, or would I love to hear your thoughts?