LUKE: I hate that building.
LORELAI: What, the school?
LUKE: Three years of going there, I have no good memories.
Luke attended Stars Hollow High School for three years, meaning he didn’t complete the full four years of high school available in the US. He may have dropped out of school (sixteen was the legal age for this in Connecticut at the time), or done his last year of education at a trade school. From a conversation Luke had with the school principal, the second one seems the more likely.
If Luke regrets not doing four years of high school, then it might explain why he is so insistent that Jess remains at school. There is some irony in the thought he is forcing Jess to attend the school that he himself supposedly hated, when Jess is miserable there.