When Jess visits Rory at her grandparents' house the worst of Logan's entitlement and pompousness comes to the fore.
He verbally berates and tries to goad Jess into a fight, which doesn't work but does cause Rory to reevaluate her life and their relationship.
Through that event, Rory becomes fascinated with Logan.
She sees him in a different light after seeing how the other members treated him.
All I see is one door, and I'm being pushed through it. You try living without options” Logan is a charming, smart, flirty, and witty young man, who in reality has very low self-esteem.
He likes romantic gestures and can be kind, as when helping Luke who neglected to get Lorelai a Valentine's Day present. Logan's appearance in the newsroom was uncommon and an annoyance to Doyle Mc Master, the editor of the Yale Daily News.
Rory is highly embarrassed and angered at Logan for doing such a thing.
Rory later gets him back by enlisting her grandfather to trick him and his friends into thinking that Logan's parents and Rory's grandparents were planning for their wedding. His parents mistreatment of him resulted in his low self-esteem, which comes to the fore when he feels threatened, for instance by other guys who show interest in Rory. He grew up looking at a preordained life, which shaped him in his zest for living in the moment and lead a life of reckless fun for as long as he possibly can.However, Logan does not pay heed to what his family says and still stays with Rory.During Rory's break from Yale, Logan help keeps her distracted by involving her in his hedonistic life style, often footing the bill.Rory, then, calls Mitchum and tells him that she "disapproves" of his behavior.