I think the answer to this is to look at what BOTH movies are telling us.
Han: I know every time … every time you look at me you’re reminded of him
Leia: You think I want to forget him? I want him back.
Han: There is nothing more we could have done. There’s too much Vader in him.
Leia: That’s why I wanted him to train with Luke but… I just never should have sent him away. That’s when I lost him. That’s when I lost you both.
Han: We both had to deal with it in our own way. I went back to the only thing I was ever any good at.
Leia: We both did.
Han: We lost our son, forever.
Leia: No, it was Snoke. He seduced our son to the dark side. But we can still save him. Me… you.
Han: If Luke couldn’t reach him how could I.
Leia: Luke is a Jedi. You’re his father. There’s still light in him, I know it.
Rey: Master Skywalker, we need you to bring the Jedi back because Kylo Ren is strong with the dark side of the force. Without the Jedi we won’t stand a chance against him.
Luke: What do you know about the force?
Rey: It’s a power that Jedi have that let’s them control people and make things float.
Luke: Impressive. Every word in that sentence was wrong. Lesson one, sit here, legs crossed. The force is not a power you have. It’s not about lifting rocks. It’s the energy between all things. The tension… the balance that binds the universe together.
Rey: Ok. But what is it?
Luke: Close your eyes. Breathe. Now, reach out.
Rey literally reaches out her hand and Luke used a long leaf to tap her hand. Rey gasps.
Rey: I feel something.
Luke: Do you feel it?
Rey: Yes, I feel it.
Luke: That’s the force
Rey: Really?
Luke: Wow, it must be really strong with you.
Rey: Oh, I’ve never felt any…
Luke hits Rey’s hand with the leaf.
Rey: Ow!
Rey looks at him hurt and he looks back and her and then she realizes her mistake.
Rey: You meant reach out like… I’ll try again.
Luke: Breathe. Just breathe. Reach out with your feelings. What do you see?
Rey: The island. Life. Death and decay that feeds new life. Warmth. Cold. Peace. Violence.
Luke: And between it all?
Rey: Balance and energy. A force.
Luke: And inside you?
Rey: And inside me, that same force.
Luke: And this is the lesson. That force does not belong to the Jedi. To say that if the Jedi die the light dies is vanity. Can you feel that.
Rey: There’s something else. Beneath the island. A Place. A dark place.
Luke: Balance - powerful light, powerful darknes.
Rey: It’s cold.
The rock breaks and the pebbles on the rock start to float.
Rey: It’s calling me.
Luke: Resist it, Rey. Rey! Rey!
A wave blows up through the whole and breaks Rey’s concentration. Rey gasps for breath.
Luke: You went straight to the dark.
Rey: That place was trying to show me something.
Luke: It offered something you needed… and you didn’t even try to stop yourself.
Rey: I didn’t see you. Nothing from you. You’ve closed yourself off from the force. Of course you have.
Luke: I’ve seen this raw strength only once before, in Ben Solo. I didn’t scare me enough then, it does now.
Luke: Lesson two. Now that they’re extinct, the Jedi are romanticized, deified. But if you strip away the myth and look at their deeds, the legacy of the Jedi is failure, hypocrisy, hubris.
Rey: That’s not true.
Luke: At the height of their powers, they allowed Darth Sideous to rise, create the Empire and wipe them out. It was a Jedi master who was responsible for training and creation of Darth Vader.
Rey: And a Jedi who saved him. Yes, the most hated man in the galaxy, but you saw there was conflict inside him. You believed that he wasn’t gone, that he could be turned.
Luke: And I became a legend. For many years there was balance, and then I saw… Ben, my nephew, with that mighty Skywalker blood. In my hubris I thought I could train him, I could pass on my strengths. Han was… Han about it, but Leia… trusted me with her son. I took him and a dozen students and began a training temple. By the time I realized I was no match for the darkness rising in him, it was too late.
Rey: What happened?
Luke: I went to confront him and he turned on me. (Vision - Luke: Ben, No! - shows unarmed Luke and unarmed Ben maing the hut collapse) He must have thought I was dead. When I came too, the temple was burning. He had vanished with a handful of my students and slaughtered the rest. Leia blamed Snoke, but it was me. I failed… Because I was Luke Skykwalker, Jedi Master… a legend.
Rey: The galaxy may need a legend, I need someone to show me my place in all this. And you didn’t fail Kylo. Kylo failed you. I won’t.
Rey: I’d rather not do this now.
Kylo: Yeah, me too.
Rey: Why did you hate your father? Do you have something? A towel or something you can put on? Why did you hate your father? Give me an honest answer. You had a father who loved you, he gave a damn about you.
Kylo: I didn’t hate him.
Rey: They why?
Kylo: Why what? Why what? Say it.
Rey: Why did you… why did you kill him? I don’t understand.
Kylo: No, Your parents threw you away like garbage.
Rey: They didn’t.
Kylo: They did, but you can’t stop needing them. It’s your greatest weakness. Looking for them every where. Inn Han Solo, now in Skywalker. Did he tell you what happened that night?
Rey: Yes!
Kylo: No. He had sensed my power, as he senses yours, and he feared it. (Vision of Kylo waking up to Luke holding his green lightsaber and Luke striking and Kylo defending and then collapsing the hut).
Rey: Liar.
Kylo: Let the past die. Kill it if you have to. That is the only way to become who you were meant to be.
Rey: I should have felt trapped or panicked, but I didn’t. It didn’t go on forever. I knew it was leading somewhere… and at the end it would show me what I came to see. (let me see… my parents… please) I thought I’d find answers here. I was wrong. I never felt so alone.
Kylo: you are not alone.
Rey: Neither are you.
Luke: (from a distance) Rey!
Rey: It isn’t too late.
Kylo and Rey touch then Luke appears and the connection breaks.
Luke: Stop!
Rey: Is it true? Did you try to murder him?
Luke: Leave this island now!
Rey: Stop! Stop! Did you do it? Did you create Kylo Ren?
Luke and Rey fight until Rey grabs the saber and Luke stumbles.
Rey: Tell me the truth.
Luke: I saw darkness. I’d sensed it building in him. I’d seen it in moments during his training. But then I looked inside and it was beyond what I’d ever imagined. (Vision - sound of screaming people) Shoke had already turned his heart. He would bring destruction and pain and death and the end of everything I loved because of what he will become and for the briefest of pure instinct I thought I could stop it. (Vision - luke draws and ignites his green lightsaber). It passed like a fleeting shadow and I was left with shame and with consequence and the last thing I saw were the eyes of a frighted boy whose master had failed him. (Vision - Kylo sees Luke and they lock eyes and then Kylo draws his blue saber and strikes at Luke. Luke: Ben, No. Then Kylo brings down the hut)
Rey: You failed him by thinking his choice was made. It wasn’t. There’s still conflict in him. If he would turn from the dark side that could shift the tide. This could be how we win.
Luke: This is not going to go the way you think.
Rey. It is. Just now, when we touched hands, I saw his future. As solid as I’m seeing you. If I go to him, Ben Solo will turn.
Luke: Rey, don’t do this.
Rey stands and offers him the lightsaber. Luke looks away
Rey: Then he’s our last hope.
The Millenium Falcon flies off. Luke changes to his white robes, goes to the tree and ignites a torch, then sees Yoda
Luke: Master Yoda.
Yoda: Young Skywalker.
Luke: I’m ending all of this, the tree, the texts, the Jedi. I’m going to burn it down.
Luke goes to the tree but hesitates.
Yoda: Hm.
Yoda raises a finger. From the clouds above, lightning strikes the tree and it catches fire.
Yoda: [laughing] Ah, Skywalker, missed you have I.
Luke tries to go in to save the text but a gout of flame pushes him back.
Luke: So it is time for the Jedi Order to end.
Yoda: Time it is… for you to look past a pile of old books.
Luke: The sacred Jedi texts!
Yoda: Oo? Read them have you?
Luke: Well… I…
Yoda: Page turners they were not. Yes, yes, yes, wisdom they held, but that library contained nothing that the girl Rey does not already posses. Hm. Skywalker, still looking to the horizon. Here, here, now, the need in front your nose. Hm!
Luke: I was weak, unwise.
Yoda: Lost Ben Solo you did. Lose Rey we must not.
Luke: I can’t be what she needs me to be.
Yoda: Heed my words not did you. Pass on what you have learned. Strength, mastery, hm! But weakness, folly, failure also. Yes failure most of all. The greatest teacher failure is. Hm. Luke, we are what they grow beyond. That is the true burden of all masters.
Leia: Luke. I know what you are going to say. I changed my hair.
Luke: It looks nice that way. Leia, I’m sorry.
Leia: I know. I know you are. I’m just glad you’re here… at the end.
Luke: I came to face him, Leia, and I can’t save him.
Leia: I held out hope for so long, but I know my son is gone.
Luke: No one is every really gone.
Well, that is as close as I can get barring an official script
The key is Ben’s fall. The dialog from TFA between Han and Leia shows he was heading down the dark path before Luke ever started training him. Snoke had already gotten to him. Luke believed he could correct it by following the Jedi training. But he saw hints during training but never imagined that it was too late. Ben had used the training to find others like him and they killed the rest and fled after the hut incident.
One of the keys is to see how Hammil acts the scenes. Luke is not crushed because a student turned. He is crushed because it was his nephew, Leia’s son. He is crushed because he was sure he could stop it but it was already too late. Leia rightly blamed snoke, but for the man who had saved his father, the most hated and evil man the galaxy had known (they didn’t really know Sideous), to lose his nephew like that is a blow that he couldn’t take. In the movies he says he went to the island to die, but, like other Jedi masters and like himself in regards to the full truth about the fall of Ben Solo, I doubt we got the real truth. I think he went to Ach-to looking for answers and when he didn’t find them in the greatest wisdom of the Jedi, he sank his X-wing and decided to live the rest of his life in solitude. We saw in ANH how he hungered to learn anything about his father. Owen and Beru tied him to Tatooine and only their deaths set him on the path. He cherishes family. We saw that again as he talked with Leia in ROTJ. That was the trigger that lead to him channeling the dark side to defeat Vader. Family is what turned Anakin both to the dark side and back again. Luke could not save his nephew and was crushed. He did not fear the raw power Ben had shown (contrary to what Kylo tells Rey) but he fears that same raw power in Rey.
So, given the above dialog (that the way the lines are delivered), the fall of Ben Solo was set in motion before he ever went to study with his uncle and Luke was no match for the darkness that Snoke had sparked. The fall of Ben Solo was a certainty, not a maybe. He had already fallen, he just hadn’t revealed himself yet. From his worship of Vader’s helmet, and the dialog in TFA, he wanted to follow his grandfather into darkness. And Luke completely missed all of it, like the PT Jedi missed Darth Sideous right under their noses. When you put everything together, Luke’s failure is epic. Luke should have been training Kylo from his childhood, not when Han and Leia were having problems with him. There is a reason the Jedi started the training at a very young age.