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.
The sacrifice of Leia's Jedi training came at the expense of protecting her only son, Ben Solo, from harm's way. An alleged leak, via Inverse, from Star Wars: Episode IX - The Rise of Skywalker's abandoned plotlines sidelines Leia's Jedi training for the sake of her child.
Abrams says Princess Leia chose not to train in the ways of the Force. In the films, while Luke trains to become a powerful Jedi, Princess Leia is kept busy by essential duties of her own. Later, as the leader of the Resistance, General Organa has her hands full with tasks that don't involve any use of the Force.
Even though Leia's Jedi training didn't last long, she was able to retain much of what she had learned. She was still very much in tune with the Force, so even though she wasn't technically a Jedi anymore, she could pass her knowledge on to Rey. Technically, she isn't a Jedi. But she has the ability to train one.
Yoda may have wanted to train Leia instead of Luke, but he was wrong - precisely because he did not understand that the redemptive love of a son towards his father was what would bring balance to the Force. Fortunately, the will of the Force won out, and Luke was the one chosen to train as a Jedi instead of his sister.
5. Love triangles and awkwardness — The Empire Strikes Back wasn't the first inkling that Luke and Leia had feelings for each other. Their romance was heavily alluded to in A New Hope, what with all of Luke's suggestive facial expressions to Han whenever Leia was around, and Han's clear attraction to Leia.
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.
During the iconic opening moments of Star Wars: A New Hope, Darth Vader has a tense confrontation with Princess Leia, an adversary who, unknown to him, is actually his daughter. Despite participating in Leia's interrogation, the Sith Lord doesn't uncover his familial connection with the rebellious royal.
Jedi Master Yoda is the most powerful of them all. This should come as no surprise, as he was the head of the Jedi Order in the prequels and was revered for his abilities during the original trilogy. Yoda's power is unmatched and was a real threat to Darth Vader and the Imperials.
Not only was Leia incredibly strong-willed, but she also had the blood of the Chosen One coursing through her veins. This knowledge, paired with some more recent lore tidbits, suggests she was one of the most powerful Force-users to exist, perhaps even surpassing Luke.
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.
She thought she could remember Padmé - describing her to her brother Luke as "kind but...sad." But in truth Leia seems to have been confused, instead remembering Padmé's former handmaiden (and doppelgänger) Sabé. But Leia actually knew quite a lot about Padmé.
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.
Description. Leia Organa wielded a blue-color lightsaber during her year of training. Leia Organa's lightsaber was a blue-bladed lightsaber powered by a kyber crystal in the core of the hilt. It was silver and copper in color and featured mother-of-pearl inlays.
Even though Leia was rather advanced for her age, having learned to speak and walk before the age of one, she did not show any signs of Force potential—much to the relief of her adoptive father, who knew that being a Force-sensitive in Palpatine's Empire would be a heavy burden.
This continued until Leia sensed trouble ahead and hoped that giving up her Jedi training would avert a deadly fate for her son Ben. Luke kept Leia's lightsaber, hoping to pass it on to a worthy recipient. It's the Force ghost of Luke Skywalker that gifts the Leia Organa lightsaber to Rey in The Rise of Skywalker.
Plo Koon. Wise and compassionate, Plo Koon was one of the most effective Jedi masters, genuinely caring about the clones he commanded.
Unwilling to see his son die, Vader gave his life to save Luke, thereby dying as Anakin Skywalker. Anakin ultimately fulfilled his role as the Chosen One and brought balance to the Force, fulfilling Qui-Gon Jinn's belief in the prophecy that foretold Anakin's destiny.
1 Darth Sidious
There has been no Sith, as powerful, meticulous, nor as evil as the Emperor himself, Darth Sidious. As previously mentioned, Sidious trained in the Dark Side by Darth Plagueis before Sidious killed Plagueis in his sleep, making Sidious a Sith Master.
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.
While their affection had to remain hidden, the two kept in frequent contact, even throughout the Clone Wars. But despite this, Anakin found out that Padme was pregnant only a couple of weeks before the twins were born. So, why did it take so long for her to tell him?
The Birth of the Skywalker Twins was when Padmé Amidala gave birth to Luke and Leia Skywalker. She died soon after, her last words saying that their was still good in Anakin, who had recently become Darth Vader.
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.
So Luke offers Grogu a choice by putting a piece of Mandalorian net armor (given to him by The Mandalorian earlier in the episode) and a small lightsaber before him. Luke said that the lightsaber was the same one owned by Yoda.