I dug out some of my old writing and found that 2016 me wrote why I ship Conneree, and I know a lot of people that follow me like Conneree, so I'll share it.
(This is mostly based on TLOS 3 Bree aka. that one book when her characterization wasn't completely crap.)
Conner and Bree are different, therefore they can balance each other out and help each other to grow.
Bree is cool and calm and resourceful, while Conner is awkward and panics more. Bree is able to keep a cool head in times of trouble, while I feel like Conner is more affected by his emotions and worries like "what do I do" "what will happen". Conner can help Bree be more sensitive, and Bree can help Conner to think logically.
Bree is like the cool, new generation with all those shiny technology, and Conner is more traditional, preferring books and handwritten stuff. Bree can represent the present and Conner can represent the past and they combine to create something better for the future!
Conner is brave and selfless while Bree is not as brave (*cough* how she let the Masked Man take advantage of her *cough*).
Bree is a great liar and I think she keeps her real feelings to herself (to prevent herself from being hurt?), while Conner wears his heart on his sleeve, is a bit naïve and trusts people easily. I headcanon Conner is a good actor, but he can't lie very well. Bree is probably attracted to Conner's genuine show of feelings. In my fanfiction 7 Days, I also headcanon-ed that Bree is not very good with dealing with her feelings, and she feels confused about them, so she develops into a great liar to hide them. Conner is one of the exceptions that wins a place in Bree's heart.
Conner is also emotionally stronger because he's more cheerful, while Bree, not so much (at least I think). He can help with her in this aspect.
Conner is naturally optimistic and a bit idealistic, while Bree is realistic. Bree can bring a bit of realism in Conner's world, and he can show her the possibilities.
There's also the fact Bree can absorb new things quickly (as seen from the bathroom scene in TLOS 3), and Conner has a lot of crazy possibilities in his head, so Bree can probably understand Conner and his ramblings.
Conner and Bree also have some similarities, like how they both advocate strongly for things they believe in, and how they're both writers. I guess they can connect a lot because being a writer is hard, and when your significant other is a writer, it can make things easier.
They also can be blunt about what they think, as Conner is painfully honest, while Bree questions everything in a straightforward way.
They have also known each other for a long time (at least since middle school) so they are probably super familiar with each other after years and years of being friends/ lovers.
Bree and Conner also both know about the Land of Stories and the Otherworld. Both of them ultimately feel more connected to the Otherworld, but they still feel something for the Land of Stories, so they can talk about it.
Both of them crave adventure and excitement, and because they can't really get that in the Otherworld, they turn writing and the Land of Stories. They can bond over it.
Plus, Bree has some of Mother Goose's blood in her, so it will be like Mother Goose's granddaughter and the Fairy Godmother's grandson getting together. Like two best friends' offspring getting married.
Conner and Bree still have a crush on each other even if they hadn't seen each other for a year, which means they do actually like each other and it's not a casual crush, and so they have potential to develop a relationship.
At the end of TLOS 3, Conner asked what excuse Bree will tell her parents for running away, Bree replied with, "That I fell in love with a circus clown and followed him around Europe." But that is technically the truth as Bree likes Conner and Conner is funny like a clown, and they DID go around Europe... well talk about an indirect confession.
So basically, I ship it! 💕