the main reasons why i ship coai
to me, coai/ shinshi is just the healthier ship, filled with trust, understanding, and mutual interests. it's also the one ship i can see lasting long term in the real world.
they are partners/ solve cases together: Ai likes when he rambles his deductions calling him a "sparrow" (file 713 & 714), though she isn't afraid to ask him for clarification if his explanations get too convoluted. He doesn't really need to help her understand the case, she can figure it out on her own most of the time (file 466-469, 656 [he smiled when he was listening to her deduction]) nor does she give up before she puts any effort into solving the problem first (file 548, 713). She actively contributes to his deductions and he always asks her if she has any ideas (file 287, 525, 664, 729). he can depend on her to stay calm under investigations (file 729, 870) and come up with plans to protect/ help the DB if conan can't be there (file 549, 817). she shares his same investigative curiousity and isn't a bystander, sharing her biochemist background to help shinichi's deductions (file 1098).
they help each other's overcome their weaknesses/ fears: her trust-issues & self-blaming tendencies (file 189-191, 344-346), his impatience & impulsivity (file 429, 475). they put each other at ease when it comes to being paranoid about BO members in public (file 287, 289, 359, 624, 680, 741 [he asked if she wanted to sleep over at the detective agency??], 775, 1006). As for the lies regarding the BO between the two, shinichi said it best in file 341: "[Haibara's] not as tough as she looks." They protect each other because if haibara tells conan about the BO he'll be impulsive/ wanting to attack them immeadiately and if conan tells haibara BO stuff before he resolved it, her trust issues would go on overdrive. Though it should be noted that haibara eavesdropped on some things, so she understands that conan's hiding things from her, by nature that she's the BO "traitor" she's hiding things from shinichi too.
they accept each other imperfections: they tease each other about being adults in a kid's body (file 515-517,724), shiho's age, his lack of tact, his tone-deafnesses, his relationship with ran, her fangirling higo, her aloofness/ sarcasm (file 680), etc. they can get angry with each other and apologize to each other, while maintaining a healthy competitive relationship. she loves being able to challenge him intellectually such as telling him to guess her favorite song and the code in file 491, while he's always up for the challenge (file 200) since she knows that shinichi likes puzzles.
he always notices and likes when she smiles (file 275, 292).
shinichi is protective of her and she's protective of him (file 238- 242, 346, 429, 582, 624, 681, 824, 1070) but not in a possesive way & he doesn't need to be told to do so, it's automatic at this point. he promised to always protect her and he kept it.
shinichi always knows when shiho looks like she's going to run away. he always hopes that she doesn't but he always runs after her anyways just to make sure (file 289, 346, 437, 817).
he defends her family when other people make negative comments about them (file 425, 1072).
they share interests other than the BO (soccer, pop culture, animals, music, history, etc.) but they're individuals first.
their relationship has boundaries: haibara respects shinichi's feelings for ran / navigates her jealousy rather gracefully (file 313, 999,1000). conan doesn't probe further about her past with gin when she doesn't want to answer (file 242). they keep each other in check (file 242, 515, 1091). they never force each other to reveal secrets they're not ready to share (file 341) and she can tell when he's suppressing his emotions/ concerns (file 609).
they rescue each other even though they can rescue themselves without each other (file 755,817). she can guess where he'll be/ gives him a spare antidote (file 654) and he always has a plan to get her to safety (file 429, 824). haibara can predict conan's behavior and vice versa (file 289, 430).
side note: it's canon that ran ships coai (file 876), which is hilarious because ai ships shinran (mainly out of denial/ love bc she wants shinichi to be happy/ ran looks like her sister so she wants her to be happy, but this is a whole seperate discussion). also the DB always noticed a vibe between coai, especially ayumi and Mitsuhiko.
for those interested, there's a parallel to shinran: in file 887, haibara ai guessed conan's phone passcode correctly on the first try. whereas it took ran in file 483 multiple tries just to get it correctly. in non-canon movie 16th, conan saw ran's underwear and said 'white' out loud, in canon file 714, he saw haibara's underwear and also said 'white' out loud and he got defensive when she called him a pervert.
