RORY: You’ve never been a part of an actual graduation ceremony.
LORELAI: I know. That’s because my stupid conservative high school wouldn’t let me be in the ceremony and nurse you at the same time.
We discover here that Lorelai did not graduate from her private high school. Although she jokes they wouldn’t let her graduate while nursing a baby, most likely she was actually asked to leave once her pregnancy became obvious. Her former classmate Mitzi said she hadn’t seen Lorelai since “her seventh month”, suggesting that she didn’t return to school after the summer vacation of 1984.