Why does Yoda opt to hide in the jungle for the rest of his life, while Obi-Wan Kenobi opts to return and fight?

Question

Once a famous and active jedi, Yoda hides on the remote swamp planet of Dagobah. He agrees to train Luke (quite reluctantly) but does not even think to come back himself to support Rebels. He is one of the best between all masters of the Force remaining, the Rebels would really benefit from having him in command. Nothing seems to be preventing him from piloting an interceptor, for instance.

Of course, there is a risk of him being captured and this is probably why he's in hiding, but this is also true for Luke, Leia, Solo, Obi-Wan Kenobi and likely many other rebels that do not run away.

This is also very different from Obi-Wan Kenobi who comes back when called, while he knows it is dangerous for him.

Why does Yoda opt to hide in the jungle for the rest of his life, while Obi-Wan Kenobi opts to return to fight?

Answer 1

Obi-Wan did not 'come back when called' or 'opt to return to the fight'. He responded to Princess Leia's desperate call for help and intended only to return the two droids C3PO and R2D2 to Leia's father on Alderaan. He just happened to get dragged into the fight when captured by the Death Star.

Just after Order 66, Yoda was considered the most experienced Jedi Master left alive, so he went deep into exile. Not only to hide himself from being sensed by the Sith Lords. But also so that he can complete the training for the new Jedi (Luke or Leia).

Obi-Wan, on the other hand was not as strong with the Force, so he didn't need to be as secluded as Yoda, so he elected to watch over Luke on Tatooine. The whole idea was that he would train Luke when he grew up, and then Yoda would finish the job. But since Leia asked for help, and Luke wanted to leave Tatooine anyway, they left together and Obi-Wan trained Luke on the go.

When the Millennium Falcon got captured by the Death Star, Obi-Wan knew that Vader would most likely prevent them from escaping, and thus, he faced Vader to give Luke the chance to escape.

Yoda, on the other hand knew that he would have to wait for the next Jedi to appear, so he could train him. When Luke came to Dagobah, Yoda did train him, but not to the fullest. Yoda's job wasn't finished yet when Luke left to help his friends on Cloud City, so Yoda couldn't go haring off to help and support the rebels yet. Only when Luke came back months later, did Yoda see that his training was indeed complete (or almost). But by that time, Yoda was dying and too weak to help the rebels.

In summary, Obi-Wan and Yoda both meant to train Luke as their main job. Obi-Wan just got the opportunity to try to help the rebels a little along the way, whereas Yoda died once he finished his job. Neither could help the rebels before Luke's training was complete, because had they been caught or killed, there would have been noone left to pass on the Jedi legacy.

Answer 2

1. Yoda wasn't up to defeating the Sith, which was pretty much the main reason they needed a real Jedi.

2. As a consequence, Yoda's main job was to train up new model Jedi who would be. He realized that way back during his fight with Palpatine/Sidious at the end of ROTS.

3. The reason he is sitting in the jungle is, he's waiting for the Force to guide Luke to him.

   When right is the time for skills to be taught, to us the living Force will bring them

4. Whereas, for Obi-Wan, the Force already did so, in the form of R2-D2 and Leia's amazing, singing hologram.

ROTS novelization by Matthew Stover covers it in detail.

In that lightning-speared tornado of feet and fists and blades and bashing machines, his vision finally pierced the darkness that had clouded the Force.
Finally, he saw the truth.
This truth: that he, the avatar of light, Supreme Master of the Jedi Order, the fiercest, most implacable, most devastatingly powerful foe the darkness had ever known …
just—
didn’t—
have it.
He’d never had it. He had lost before he started.
He had lost before he was born.

The Sith had changed. The Sith had grown, had adapted, had invested a thousand years’ intensive study into every aspect of not only the Force but Jedi lore itself, in preparation for exactly this day. The Sith had remade themselves.
They had become new.
While the Jedi—
The Jedi had spent that same millennium training to re-fight the last war.
The new Sith could not be destroyed with a lightsaber; they could not be burned away by any torch of the Force. The brighter his light, the darker their shadow. How could one win a war against the dark, when war itself had become the dark’s own weapon?
He knew, at that instant, that this insight held the hope of the galaxy. But if he fell here, that hope would die with him.
(Chapter 20)

and

“My failure, this was. Failed the Jedi, I did.”
He spoke to the Force.
And the Force answered him. Do not blame yourself, my old friend.
As it sometimes had these past thirteen years, when the Force spoke to him, it spoke in the voice of Qui-Gon Jinn.
“Too old I was,” Yoda said. “Too rigid. Too arrogant to see that the old way is not the only way. These Jedi, I trained to become the Jedi who had trained me, long centuries ago—but those ancient Jedi, of a different time they were.
Changed, has the galaxy.
Changed, the Order did not—because let it change, I did not.”
(Chapter 21: A New Jedi Order)

... and finally, the specific reason Yoda was freezing his old wrinkly butt off in the swamp instead of jumping around the bars, pickin' fights and cutting' hands off; or otherwise rebelling: he was waiting for the Force to bring the Skywalker children to him, for training:

“Jedi training, the sole source of self-discipline is not. When right is the time for skills to be taught, to us the living Force will bring them. Until then, wait we will, and watch, and learn.”
(Chapter 21: A New Jedi Order)

Answer 3

The Answer chosen is wrong. Obi-wan wasn't on Tatooine so he could train Luke. He was there to look after him and keep him safe from Vader. We all seen the prequels and clone wars cartoons, we know how young training is suppose to begin for Jedi's. Obi wan had opportunity to approach Luke for 18 years and try to train him but he chose to respect the Skywalkers wishes and let him be. If those droids had never shown up, then Luke would have snuck off to be a rebel pilot against uncle ownens wishes and Obi wan would never have seen him again. He only trained him out of necessity to help Princess Leia.

Its cannon that Luke is the most force sensitive being to ever exist, far more than Yoda. So why was it fine for him to be hidden away on Darth Vaders home planet but Yoda had to go to a swamp planet so he could "Train Luke or Leia". He made zero attempt to reach out to Luke or Leia and when Luke showed up he was very relunctant to teach him at first.

You're so focused on Luke's destiny to bring balance the force that you forget that this was originally thought to his fathers destiny when Obi Wan and Qui Gon first found him. But instead he ended up almost bringing about the end of he light side of the force. I'm sure that Obi Wan and Yoda could sense the potential that was in Luke but they were both relunctant to teach him because the last person they met with that level of potential was his father and they saw how that turned out.