Obi-Wan never did, but Yoda originally had wanted to train Leia instead of Luke. In the book “Star Wars: From a Certain Point of View” there is a short story from Yoda's perspective on Degobah. He was thinking to himself how he could not wait to train Leia, as she had all the qualities of a good Jedi, unlike Luke.
Because Leia is arrogant and spiteful, like her father was.
She is a symbol of the rebellion and takes orders from no one.
In short: He felt Luke wasn't ready. Yoda was the grandmaster of the fallen prequel-era Jedi Order and trained Jedi for centuries, with students typically beginning as young children. He saw too much of Anakin in the young adult, and he didn't want to end up training the successor to Vader.
First, she admitted that she didn't really care about the Force. Thus, if she went with Luke, she would be doing it for the sake of being with Luke, not because she was following the will of the Force. However, more importantly, Leia refused to be a Jedi because Darth Vader's power had scared her.
Some of the (many) great moments in Empire come when Luke Skywalker is training with Yoda on Dagobah, but of course, the film makes it clear that Yoda was initially hesitant to train Luke. But it turns out that he was originally far more interested in training another: Luke's twin sister, Leia Organa.
However, she ultimately decided that the best path for her to serve the galaxy left no room for the extended isolation of Jedi training," Hidalgo wrote. "Leia on her new family and senatorial politics, Luke began his travels, largely disappearing from galactic view.
Why did Vader sense Luke but not Leia? He only senses Luke when he actually using the Force, Leia is not actively aware or using the Force and therefore he does not sense her. He is also not looking for a daughter either until Luke spills the psychic beans on her later on.
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence.
Theory 1: Leia Doesn't Remember Ben Is Obi-Wan
Throughout her encounters with Kenobi in the series, he refers to himself as Ben. The most straightforward explanation would be that Leia knows the person who rescued her is Ben, and never connected the dots that Ben is actually Obi-Wan.
Leia Would Know She's Force Sensitive
We know from Leia's parents and from moments in the Star Wars sequels that she was, in fact, Force-sensitive, even though she didn't get a chance to display those powers in the original trilogy.
Vader and Palpatine didn't know Yoda trained Luke because Yoda concealed his presence from the Force. They knew about Obi-Wan, but both Vader and the Emperor thought Obi-Wan was the last Jedi. Even in the "Return of the Jedi", Vader and Palpatine thought Luke's skills derived from Obi-Wan.
Yoda preferred Leia since she seemed to posses the traits typically found in "great Jedi." As many Star Wars fans know, the Princess is strong-willed, determined, and always focused on the task at hand.
What he did not see, at the time at least, was that Padmé used her last breaths to tell Obi-Wan that she was certain that in regards to her husband, "there's still good in him." Now, those words are set to be revealed to someone other than Darth Vader himself.
According to one theory (via Reddit), the pair had a specific reason for avoiding each other: Chewbacca was observing a Wookiee mourning ritual. Based on Wookiee customs, Chewbacca could not seek comfort from others yet, but he could still work to save others.
Arguably, most Star Wars plot points revolve around characters simply not knowing something, very often about their family history. But, on top of all of that, the biggest reason Obi-Wan doesn't know Anakin is alive is that the last time he saw Anakin Skywalker in Revenge of the Sith, Ben literally left him for dead.
Even though he knows that Anakin is alive, Obi-Wan chooses not to tell Leia and his probable reasoning for doing so is likely the same for Luke: Obi-Wan might suspect his partial complicity in Anakin's final transformation into Darth Vader could turn Luke and Leia against him.
Leia does not seem to react to tragedy. Instead, she has this wonderful ability to stay perfectly alert, reasonable, and careful of the feelings of others. She witnessed the destruction of her entire planet, and still had the mental and emotional strength to escape with Luke and Obi-Wan.
She also knows Obi-Wan, and she knows him well. Her holographic plea for help, already iconic, will never be the same. She knows Obi-Wan's real name as well as his alias of “Ben.” When Luke comes barging into her cell and says, “I'm here with Ben Kenobi,” Leia jumps off the bunk in an instant.
Obi-Wan came to the Death Star to save Leia from the Empire's clutches, but was killed by Darth Vader while the others were busy escaping. Leia didn't see Obi-Wan again, nor did she experience any sadness when she learned of his death.
Reva knows that Anakin Skywalker is Darth Vader because she was one of his targets—a child—during the Order 66 killings that took place during the events of Star Wars Episode III: Revenge of the Sith.
But then we learned Padmé passed away moments after giving birth to the twins. Therefore, how could Leia have had any memories of her birth mother? But when little Leia realized Obi-Wan had known her birth mother, he shared a story that not only made Leia's memories of Padmé plausible, it made them all the more moving.
This is not because the Third Sister knows that Leia is Anakin Skywalker's child; it is because the Third Sister found a link between Obi-Wan and Bail Organa and she believed Obi-Wan would do anything to save Bail's daughter.
Leia doesn't get to reunite with Obi-Wan, and instead, just before escaping with Han and Luke, she sees his murder. Of course, Leia doesn't know Darth Vader is her father yet, either in A New Hope and certainly not in Obi-Wan Kenobi.
Yes. In the book 'Tatooine Ghost', Leia learns of Anakin's life prior to his evolution into the Darth Vader personae. This revelation leads her to forgive him. She even named her third child in memory of her father.
Leia's journey yields a time dilation of 62.6 days; however Luke experiences a time dilation of 700.8 days. The students concluded that Luke is therefore 1.75 years younger than Leia, possibly rendering them the first twins ever to have more than a year between their ages.