
These posts are starting to just become an excuse for me to use nice pictures of Jess up. Anyway, this one is less about how Jess and Rory would fit into what the show sets out to say, and more about their relationship (albeit flawed) itself.
1) Jess was the only one out of the three that treated Rory like an equal and not as property. I don't think I even need to mention how possessive Dean was, his constant aggression towards Tristan and Jess were testament to that, but Logan too, when Jess showed up in S6, his body language was immediately incredibly possessive of Rory and his uncalled for aggression towards Jess reveals his need to drive him away from Rory as soon as possible, lest she run away with him the first chance she got. This lack of faith and quite frankly, misogynistic level of possessiveness is something that Jess never displays. When he finds out that Rory was on friendly terms with Dean again, he just asks her politely to tell him so that he doesn't have to find out from local gossips.
2) Jess is the only love interest who was truly respectful of Rory. In the same incident mentioned above, Rory however, full of apologies and "nevers" and "promises", lingering habits from her relationship with Dean where she seemed to constantly have to prove herself as trustworthy and apologise to him for her friendships and actions. Even when Rory wrongfully accuses Jess of getting into a fight with Dean, he's incredibly accepting of her apology, no anger or passive aggression. Even with Logan she seems to always be treading on ice, when they first start dating she's incredibly upset at his inability to commit and later on, when he does commit, he never seems to be mindful of what she wants, never modifies his plans or actions to make her more comfortable and he does all of this under the pretence of getting her to "take risks" and "get out of her comfort zone". In S6 episode 8 where she confronts him about having been rude to Jess, he doesn't bother to apologise he just mocks her, him and proceeds to take offence to a statement that may or may not have been about him and shout at her in front of an entire restaurant. The incident reeks of the time that Dean did something similar at the Dance Marathon. Public humiliation is uncalled for and a sign of aggression, a need to assert power.
3) It is Jess who has Rory's best interests as a person and not just as his girlfriend at heart. Dean is constantly threatened by Rory's ambition. In Season 2, Rory prioritises planning for Harvard over a date with Dean and he gets incredibly aggressive and insecure. Then again in Season 3, closer to Rory's graduation, after her lunch with Harvard Alumni, Dean begins to get passive aggressive about the attention she was giving him and began giving her ultimatums about their future. He'd always been insecure about the status of their relationship when she went off to Harvard, and while that's a valid concern, he expected her to prioritise that over her ambition which shows how shortsighted he truly was. When Rory dropped out of Yale, Logan was apprehensive about the situation but accepted it pretty quickly, even throwing a party to celebrate her arrest for the yacht incident. While I understand that taking a year off college can be extremely valuable, Logan wasn't able to grasp that firstly, it wasn't something Rory would normally do. Since he was unable to catch on to that, he was unable to deal with the fact that she was afraid ( due to comments made by his family). Furthermore, the year off college aside, he seemed to see nothing wrong with her chosen lifestyle of D.A.R. meetings and cocktail parties that so closely mimicked that of her grandmother. This is disturbing because we know he comes from a family who would rather that Rory not work if she were to marry Logan. I find it shocking A 21st century boy from a good school and with seemingly progressive views saw nothing wrong with the fact that his girlfriend's life was starting to mimic that of her grandmother, who grew up in an era where women were offered far less choices and opportunities than they were in Rory's era. Its easy to draw parallels between this and Dean's constantly expressing that he wanted a Donna Reed-esque wife. Ugh. Either way, there were only two people who knew Rory well enough to catch onto the fact that there was something wrong with the way she was living her life: Lorelai and Jess. Its telling that Jess was the only other person who knew Rory as well as her mother, a clear indication of his genuine concern for her. Going back to Yale wasn't going to help his relationship with her, infact it could push them further apart. However, it was the best thing for Rory and so Jess never failed to express this.
As a conclusion, here's an interesting article on why Jess shouldn't be team Rory (something I bet a lot of people haven't considered): http://www.mtv.com/news/2927430/team-jess-team-rory-gilmore-girls/