So, what first got me thinking is when Obi-Wan says
'That boy was our last hope' and Yoda says
'No... there is another' (awesome scene, sick lighting, Yoda doesnt speak like a spastic). Obi-Wan clearly knows that Luke has a sister, and that it's Leia, so it's interesting that he says Luke was their last hope. Whereas Yoda knows this is not true. Clearly either Luke or Leia (or both) could have been trained to be Jedi right? So why only Luke?
Luke, the obvious choice:Luke grows up on Tatooine with family, being overseen by Obi-Wan. It seems like he's already been chosen at this stage in some way, as Leia is given no jedi to watch over her but instead a trusted friend adopts her.
A theory i've seen since Ep7 is that because the force flows through all living things, placing Luke on a desert planet not only helps him hide, but prevents him 'awakening' to the force on his own or accidentally having a force-fueled outburst (living a pretty quiet life). Note how Rey also appears to be left on a desert planet, with an old trusted friend of Leia etc living conveniently close.
But why does Obi-Wan think of Luke as the only hope? Perhaps it's an understandable prejudice/sense of nostalgia, Luke 'looks' like whiny teenage Anakin and even has the surname 'Skywalker', of both children Luke is the one hiding in plain sight and the most superficially similar to Obi-Wan's old friend (in fact it is this that alerts the Empire to his presence as Vader's son, whilst Leia remains hidden). But, there may be more of a reason why it would not have been a wise choice to train Leia...
Vader's daughter:Although Luke is the most superficially similar to Anakin, watching the entire saga again i realised this time that Leia has far more Vader in her than Luke does.
From the start of the film Leia is absolutely willing to kill at any given moment. Her and Han have that in common, whereas Luke (after receiving a rudimentary set of training) seems to favour the diplomatic (Padme) solution for films 5/6. The entire raid on Jabba's Palace that Luke planned is framed around the possibility of Jabba negotiating or eventually surrendering, Luke could have easily ran in and killed them all but instead he attempts to resolve it peacefully at many stages before eventually running out of options. If the raid on Jabba's Palace had been planned by Leia, you get the impression it would've been quicker and more violent.
They tease us with the Luke/Vader parallels in these films because Luke is the last Jedi and this is the narrative. Luke wears black, has a robotic hand and force-chokes a guard out of the way in Jabba's Palace, without killing them. But Leia physically strangles Jabba (they were going to blow up the yacht anyway), and sets Chewie on Lando after he frees them (she angry, look at them 'force choke' eyes)
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loginConsidering that Yoda and Obi Wan constantly harp on about Luke controlling his emotions, imagine if they were doing the same with Leia who is far more fiery than Luke. Luke never even loses his temper other than in his final confrontation with Vader. I feel it is no co-incidence that it is Leia's child that has so much Vader in him, Leia certainly got more of a dose of Skywalker than she did of Amidala.
Anakin/Leia parallels, military leadership:This goes beyond merely temperament.
One of the few redeeming traits of Anakin as a protagonist (see the 'Clone Wars' series where they actually make him a decent protagonist without changing his personality) is that he's this capable military leader who does what it takes (more than any jedi) to accomplish a mission and arguably save lives in the long term. He's a classic adventurer and even from a very young age he wanted to travel the galaxy and visit all the stars.
When Ep4 begins, Leia is already a key member of the Rebellion and they have just successfully pulled off a raid that allowed them to steal the Death Star plans. Whatever Leia's upbringing, she's already on the front lines fighting the good fight. At the exact same age, Luke is working on a farm...
'Listen, I can't get involved! I've got work to do! It's not that I like the Empire, I hate it, but there's nothing I can do about it right now. It's such a long way from here'.
Also, when faced with the possible destruction of her homeworld Leia lies and tells Vader and Tarkin that the rebel-base is on Dantooine, knowing that the world she names would be destroyed. May no longer be canon, but Dantooine is an inhabited world. Leia is capable of naming an inhabited world to be destroyed rather than reveal the location of her rebel base, not that this is a bad thing but it's certainly ruthless.
The attack on the 1st Death Star is being planned and organised by Leia, and she briefs the pilots before they fly off to fight. She does the same in ep5 before the battle of Hoth. Despite the opening titles of ep5 saying
'a group of freedom fighters led by Luke Skywalker have established a new secret base...' at no point does he actually display any leadership or any intention of leading, all of this is done by Leia whilst Luke once again just flies with the rest of the troops.
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loginLeia takes the 'General Skywalker' mantle from Anakin far more than Luke, although Anakin was also a fine pilot and we see this in Luke. We do see on Endor that Leia is also an instinctive pilot so presumably she only doesnt participate in ep4/5 because the rebellion wont allow her to fly as a key member.
How stong in the force is Leia?If we take all 7 films as equal, then she's very very strong.
In ep7 Kylo Ren, a dark jedi, attempts to rip secrets from the mind of our jedi protagonist that has only recently been awoken to the force, and reluctantly so. We have already seen that he can easily do this to even strong-willed non-force-users. He delves deep into her mind and reads her thoughts but after a brief struggle she eventually blocks him and even turns it around on Ren, showing how powerful she is. For a time Ren has been able to read her mind tho, before she turns it around.
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loginIn ep4 Darth Vader, a far more powerful Sith Lord, attempts to rip the location of the rebel base or Death Star plans from the mind of Leia. He cannot do this. She absolutely resists from the outset, despite being drugged by an interrogation droid at the same time as Vader in trying to tear into her thoughts. We do not know at this time if Leia has already unintentionally been 'awoken' to the force but she can resist Vader (without showing him that she's strong in the force).
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loginBear in mind that Vader is able to read Luke's thoughts during their final confrontation, however this may be a unique combination of circumstances or Luke being sloppy.
Conclusion:It's interesting that in the original trilogy nobody offers to train Leia. Fate intervened in Ep4 and Obi Wan never got to have a conversation with Leia, but in Ep5 force-ghost Obi Wan could have told Luke to go to the Dagobah system to be trained by Yoda, and bring Leia, but he doesnt.
I was also interested to see that from what we've seen so far in Ep7 Leia was never trained to use the force after Ep6, despite Luke saying in Ep6 that some day Leia would control powers like his. But perhaps there's a reason why she was not trained, she would have had a far harder time controlling her anger and natural Vaderness than Luke did (and he struggled).
Indeed at the end of Ep6 it is only when Vader reads Luke's thoughts he says with relish
'If you will not join me, then maybe *she* will', and that's the point when Luke loses his shit and attacks Vader in fury. Perhaps he was so protective because he could tell she would struggle to resist the Dark Side, and maybe Vader sensed this hence his excitement at the discovery.
I wonder if we'll see more in Ep8 & 9 regarding any training Leia may have received, or if she received none maybe they'll address why this was. Also part of me just wants to see Leia force-choke someone like a badass and go full Vader, but we'll see. Despite the original trilogy strongly playing the Luke/Vader parallel, Luke has always been far more temperate than Anakin and it is Leia that seemed to inherit the militaristic and angry genes from him.