While Yoda is dying in Return of the Jedi and basically undoing everything he said in The Empire Strikes Back, he tells Luke Skywalker that he didn't tell him the truth about Darth Vader because he wasn't "ready for the burden."
Now, I have to wonder, what exactly is the burden Yoda was talking about? The burden of knowing Vader was his father? That Luke would subsequently rush to fight him, unprepared? I'm thinking it goes a little deeper than that. This is all about the prophecy of bringing balance to the Force. It was never Anakin Skywalker who was meant to fulfill the prophecy, but rather his son.
It's Anakin who buys into the concept of the Dark Side. Trained in the ways of the Jedi, but only at the objections of key members from the Council, including both Yoda and Mace Windu, Anakin becomes a Sith Lord and wipes out most of the Jedi. This is fine for the Sith, because the ancient schism that led to the diverging orders had limited the presence of the Sith to only a handful of practitioners, usually a master and apprentice. I've speculated before that there were probably routinely more of them hanging around, even if they were only in reserve, or proxies, or pawns. Count Dooku, for instance, or Sifo Dyas, both of whom would have had to overlap the career of Darth Maul under Darth Sidious (that is to say, Palpatine, the Emperor). The Jedi always had far more practitioners, including a training academy with rigorous standards for admittance. The thing is, it didn't really matter, then, if Vader killed every existing Jedi. He would have to affect the Force itself, how it was perceived.
To a certain extent, he succeeded in that goal all too well. In a span of a few decades, knowledge of the Force had been almost completely forgotten or marginalized. The Jedi are dismissed as an "ancient religion" by one of Vader's Imperial colleagues, even though Vader himself actively practices a variation on it. Han Solo calls it a "hokey religion." In fact, the common description of the Force as a religion is a telling one, too. It apparently requires belief to sustain its existence, at least in the popular imagination.
That's what the Sith always wanted, likely, to keep knowledge of the Force hidden and suppressed. It wasn't Darth Sidious who created the Sith sect, but no greater adherent was ever likely to be found, someone who used it brilliantly, who rarely used his skills even though they remained great. When Vader destroys the Jedi Order and its remaining Knights go into hiding, the Sith have effectively turned the Jedi into a mirror of itself. This itself would not create a balance, but a staging ground. Both sects still remain. It has become a stalemate.
Vader seems fine to be in a relatively passive position. Star Wars fans tend to distort the record a great deal, and Vader is a prime example of that, along with Boba Fett. Both became instant icons even though all evidence in the material itself suggests no one around them really thought they were so special. Vader is really no different than Darth Maul. In The Phantom Menace, the Trade Federation only becomes aware of his existence after Darth Sidious dispatches him to work in the field. Perhaps a fitting role for an apprentice, but Vader is hardly hiding away the way Darth Maul was, waiting to do something. He's a key member of the Imperial hierarchy, Governor Tarkin's right hand man. He leads troops and commands every situation unquestionably on missions. No one is surprised when he uses the Force, but he doesn't appear to use it often. He hides in plain sight.
Luke, on the other hand, approaches the Force not as a matter of course but as a tool. He uses it like a trick, a get-out-of-jail-free card at every opportunity, whether it's reaching his lightsaber on Hoth or leaping out of the carbon freeze apparatus in Cloud City. He's reckless and never really considers it an art, and certainly not a religion. He sees no difference between his father and Yoda, and only rejects the Emperor's request to join him when he considers what he can lose rather than what he might gain. Anakin was the complete opposite. All his talk of loss only leads him to want more. Anakin fears, but it's Luke's fear that dominates events. Loss was a matter of course for him. He never knew his birth parents.
He brings balance to the Force because he rejects everything that he's told about it. For him, a Jedi is no different from a Sith. That's the key difference. It's not even that he never knew the system that caused all the problems to begin with, the one Anakin had to break. Luke doesn't repair it. He transcends it. He ends the schism. Once more, it's just the Force. But the Force is no longer a religion, worshiped by its practitioners. It's a means to an end.
The burden Yoda spoke of? Yes, it was a matter of confronting the truth about his father, about Luke's own past. But it was a past that extended far past the Skywalkers, something Yoda could never talk about with him, either of them, really. Yoda and Mace Windu wanted to reject Anakin, but they were the ones who most keenly understood what was happening to the Jedi, even if they didn't know why. It was the Sith growing stronger. It was the Sith threatening to do from the other end what the prophecy needed to accomplish. Had Luke known any of this, had he decided to side with the Emperor, the Force would remain a mystery. It would become what the Emperor wanted, what even the Jedi wanted, some sacred tradition that needed to be protected. Yoda and Mace knew Anakin had selfish motives. Yoda knew Luke had them too. That's what he wanted to avoid. But Luke's yearning came from a different place, one that was only possible after his father lost his own inner struggles. Luke understood all too well what needed to be done.
The burden he never needed Yoda to explain was one that didn't consider the Force at all, but a need he had to repair something that had nothing to do with it, to allow someone to fix a mistake on their own. To no longer rely on the Force. To remove it from the idea of a religion. To free it. To bring balance, not between competing sects, but within its practitioners.
Was Luke ready? More ready than Yoda thought, perhaps.