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In The Last Jedi Luke agrees to train Rey he says that he is going to:

Teach her three lessons:
Lesson 1: He teaches her about what the Force really is
Lesson 2: He explains to her why the Jedi should end

So whats the third one? Is it ever explained?

marked as duplicate by Edlothiad, TheLethalCarrot, Null star-wars Dec 29 '17 at 14:52

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This is apparently covered in a large deleted scene which includes Rey running down a beach with the lightsaber ignited. I'm not sure how true it is but I've seen numerous articles claiming the same. In short the third lesson is:

A true Jedi will only act to maintain balance.

Here's what the article has to say in full including some reasoning behind why they cut the scene.

Luke Skywalker’s Last Lesson To Rey

One of the biggest deleted scenes involves another lesson Luke Skywalker gives to Rey, taking place chronologically after they talk inside the cave where Luke mentions Darth Sidious. Rey notices boats arriving at the island and there appears to be a big fire from where they’re landing. Luke tells her that it is a group of bandits who regularly come back to the island to plunder and kill the caretakers. Rey is very concerned and wants to help them, but Luke tells her that if you help them now, the raiders will come back stronger and it will make things worse in the future. He asks Rey if she is always going to be here to protect them, saying that a true Jedi Knight would do nothing and would only act to maintain balance, even when people get hurt.
Rey, furious at his reasoning, ignites her lightsaber and runs really fast, a Force-powered run that we glimpsed in one of the featurettes about the making of the film (see the screenshot at the top of this article). She runs over rocks on shallow water and bursts through a door with her saber into the village square ready for battle. Luke yells for her to wait, but she doesn’t stop.
She is surprised to learn that it’s not a raiding party, but an actual party, with caretakers celebrating and swinging glow sticks. This piece of concept art from The Art of Star Wars: The Last Jedi shows what the scene looks like. The caretakers all stop and look at Rey, confused. One of the caretaker motions her her glow stick and Rey swings her lightsaber, imitating her movements, and sighs. The caretakers resume partying. Rey spots Chewbacca sitting at the party with a bunch of Porgs and R2-D2 (wearing a festive necklace). “Seriously?” Rey says to Chewie before storming out to find Luke.
Rey is mad that Luke lied to her and she confronts him. He admits that he’s sorry, but that she ran so fast and he couldn’t stop her. Rey says that she thought they were in danger and tried to do something. Luke responds, seriously this time, that that’s exactly what the resistance needs – not some old husk of a failed religion. He was again trying to teach her a lesson. Rey cries, explaining that her real friends are really dying and “that old legend of Luke Skywalker that you hate so much, I believed in it.” Luke is in shock. He realizes that he pushed her too far. Rey tells him she was wrong about believing in him and storms away.
The scene gave a further motive for Rey to want to leave the island. The caretaker party joke apparently wasn’t very funny, but the real reason the scene apparently didn’t make the final cut is that Luke ended up coming off like an even bigger asshole. Even though the basic details were approved by the Lucasfilm Story Group, it somehow didn’t feel authentic to the Jedi “code”.
/Film, Star Wars: The Last Jedi Deleted Scenes: Everything We Know

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