It is revealed that it was all a plan made by Obi-Wan, Yoda and Mace Windu, who decided to fake Obi-Wan's death so he could pretend to become a member of a looming Separatist plot to kidnap Palpatine.
This was the passage: “[Vader] lunged forward, feinting, and then slashing in a deadly downward arc with the saber. It struck home, cutting Kenobi cleanly in half.” From the movie, we all know that Vader just ended up cutting the blade through Obi-Wan's mid-section, and then Obi-Wan's body disappeared.
In A New Hope, Obi-Wan Kenobi allowed himself to be struck down by Darth Vader during their fight on the Death Star. The blade mysteriously caused the hero to disappear, which surprised even the fallen Skywalker.
Obi-Wan's “Funeral”
In the Clone Wars episode 'Deception,' Obi-Wan Kenobi fakes his death to investigate an assassination plot against Chancellor Palpatine. To successfully pull the mission off, Obi-Wan keeps his plans to go undercover close to his chest, telling only Yoda and Mace Windu of his intended plans.
He sacrificed himself to help Luke, Leia and Han escape the Death Star. He didn't want Luke to become embroiled in the fight. He knew he was going to lose eventually.
He does. Right at the end. With Luke crying over him and Vader sensing his anguish and pain he had inflicted on all those who had cared for him.
In addition to getting older, Obi-Wan's life as a whole has slowed down considerably. He hasn't been using the Force, nor has he been training padawans or saving the galaxy from the Sith. With these things in mind, it makes sense for Obi-Wan to be rather weak in his new Star Wars show.
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.
Obi-Wan knew it was only a matter of time. So, he made the difficult decision to use his learnings and become one with the force, rather than let Vader decapitate him.
Many parries, rolls, and slashes later, Obi-Wan bids goodbye to his ex-apprentice with the words, “Then my friend is truly dead,” echoing another hero who will one day try to redeem Darth Vader.
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.
Many are often shocked to find that Obi-Wan was only 57 years old when he died fighting Darth Vader in A New Hope.
In the story, we learn that Obi-Wan took on the name Ben because it's a nickname given to him by an old flame, the Duchess Satine Kryze. He takes on the name because it still has emotional resonance for him.
Yoda also senses Anakin falling even deeper into loneliness. With the death of Obi-Wan, Yoda senses that the galaxy is rapidly becoming emptier and emptier. Yoda is then menaced by two more probe droids. Yoda uses the Force to summon lightning and destroy the droids.
Why does Obi-Wan Kenobi age like that? Because he's not real, and is a fictional character played by different people. You see, Obi-Wan Kenobi is played by Alec Guinness in the original trilogy. Guinness was 62 when he filmed A New Hope, and he died in 2000.
Amongst those in attendance was Kenobi's former Padawan Anakin Skywalker, Skywalker's Padwan Ahsoka Tano, Jedi Master Plo Koon and Duchess Satine Kryze of Mandalore who could be heard crying.
He suspected that interacting longer with Obi-Wan could still bring back Anakin Skywalker, which would very likely spell the end of his reign and the Galactic Empire. Similar to how gradually turned Anakin against the Jedi, he continued to do so by manipulating him long after he had become Darth Vader.
For years, Vader hated Obi-Wan, having been struck down by his mentor and left for dead while also believing the Jedi had worked to turn his true love Padmé against him.
Obi-Wan greets R2-D2 and later recalls “not owning a droid.” Obi-Wan purposely withheld information from Luke in order to keep Luke from straying away. This could offer an explanation as to why he appears to not know who R2-D2 is. Further in Empire Strikes Back, neither Yoda nor Darth Vader recognizes either droid.
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.
R2 doesn't know it. It's as simple as that. He isn't present on Mustafar (he flies with Anakin but is ordered to stay at the ship. He isn't present while the slaughtering of the seperatists or the fight of Anakin/Obi-Wan.), differently to Obi-Wan and C-3PO.
The reasoning comes from, not only his fears that he isn't strong enough to defeat Vader after 10 years in hiding but the fact that facing Vader means Obi-Wan will have to face up to his greatest failure.
While Obi-Wan Kenobi was frail by the time of Star Wars: A New Hope, he was still stronger with the Force than Darth Vader.
As we know, the thing Vader hates most, is himself. The way I interpret the end of their fight in Obi-Wan, when Vader is screaming “Obi-Wan!” I think he is basically asking for him to not leave him again, and finish the job. He clearly was in no state to fight, or else he would've continued to fight Obi-Wan.