LORELAI: Yes, I have. I’ve also done the ‘chip on my shoulder’ bit. Ooh, and the surly, sarcastic, ‘the world can bite my ass’ bit, and let me tell you, I mastered them all, in heels yet.
Lorelai is referencing a famous saying about Ginger Rogers, who was Fred Astaire’s dancing partner in many musical films: “Sure [Fred Astaire] was great, but dont forget that Ginger Rogers did everything he did … backwards and in high heels”. If it did not originate with him, it was at least popularised by Bob Thaves in a 1982 Frank & Ernest cartoon.
The quote is used to imply that women often have to work harder than men to gain a similar recognition, or have to do so while maintaining a “feminine” image which requires a lot of discipline and upkeep.
In this context, it doesn’t quite make sense, unless Lorelai thinks that being a snotty ungrateful teenager counts as some sort of “work” that gets you somewhere in life, and which is made harder for girls than boys.