Star Wars : Leïa is not Luke's Sister (Short Version)
Leïa is not Luke's Sister :
1 – When Luke tells her about their family bound he starts with “you too have that power […] The force is strong in my family. My father has it, I have it… my sister has it.” Leïa never shows any sort of affinity with the force, whether it’d be in the first trilogy or in The Force Awakens.
2 – Qui Con Jin spots Anakin as soon as he arrives on Tatooine. Rey is super strong in everything. Luke’s powers are already noticeably in episode 4 as soon as he starts training. They are all good when it comes to repairing stuffs. Leïa is never seen holding a laser sword... or repairing anything (except when she fails at doing it in Empire)... or piloting a spaceship.
3 – Darth Vador never senses anything in her. In a New Hope he has every opportunity to feel or understand it but never does. In Return of the Jedi, when Han, Leïa and Luke are going on Alderaan, Luke's state "I'm endangering this mission" as Darth Vador guesses he is in the spaceship through the force. Leïa ? No. Also, Luke and Leïa kisses several times on the mouth before and after she is supposed to know.
4 – In Return of the Jedi, she isn't shocked when she learns that Darth Vador himself is her father. Neither is she shocked when she learns about his death. Luke burns Vador’s body on his own. Why not inviting his daughter ?
5 – When Obiwan tells Luke, he actually never tells him. It’s Luke who is totally lost after his fight with his father and is desperately looking for a bound that would be stronger that this one on the side of the rebels. He knows that otherwise he is going to turn to the dark side. Darth Vador’s last words confirm that the false sister idea worked. Vador didn’t have the strength of telling Luke that he had killed his sister. (Because I suppose that if Obi Wan sensed her death, Vador did too).
6 – Obiwan only answers “Your instinct serves you well,” the ambiguity of this sentence tells us everything. => He doesn't say "Yes, Leïa is your sister."
7 – In Rogue One, why would Bail Organa send his own adopted beloved daughter on a suicide mission in which she’ll be chased by her own dad who has Jedi’s powers and who most probably will spot her through the perturbations she creates in the force ? The true Leïa is close to the least qualified person for this mission.
8 – When Alderaan (Naboo ?) is destroyed, Obi Wan senses a great disturbance in the force and looks at Luke intensely. Leïa was on her home planet when it exploded and she died. The Leïa we know is a soldier sent instead of the real princess. Just like Padmé has several doubles in episode 1 & 2.
9 – We love Leïa because she doesn’t behave like a whiny princess although she is supposed to be one... maybe because she isn’t a princess.
10 – In The Empire Strikes Back , when repairing the Millenium Falcon, Han comes to kiss her, she shies away and complains “my hands are dirty.” She is stuck between remaining “Princess Leïa” or telling the truth. She feels guilty because she is lying to Han whom she loves.
11 – In The Force Awakens, Han dies because of Leïa's lie. Kylo Ren is shit with the force because he isn’t a Skywalker. And Rey most certainly is one.