LORELAI: You don’t care at all, do you?
MICHEL: To me you are the teacher in the Charlie Brown cartoon.
Michel is referring to the popular Peanuts cartoon strip by Charles Shultz, featuring Charlie Brown as the main character. In the original cartoons, adults were referred to but never drawn, and this continued with the first television special.
The 1967 Peanuts television special You’re in Love, Charlie Brown had a classroom scene which had interaction with a teacher named Miss Othmar. Her voice was represented with a wah-wah sound made by a trombone. Since then all adult voices have been represented by the trombone sound.
The reference is made by people to indicate that they’re not listening, or that what they’re hearing is going over their heads. It seems an odd thing for Michel to know about, but perhaps he watched a lot of cartoons when he moved to the US to improve his colloquial English.
The Annotated Gilmore Girls 
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