Obi-Wan Kenobi almost left the Jedi Order in Star Wars to keep his promise to train Anakin Skywalker. Following the success of the original trilogy, George Lucas found a way to continue the franchise set in the galaxy far, far away by tackling the origin story of Anakin before he became Darth Vader through the prequels. Those subsequent films revealed Obi-Wan's pivotal role in his journey, functioning as a mentor, but most importantly as a friend.
While Anakin's relationship was to Padmé Amidala was one of the main points of the prequels, understandably, considering that their love gave birth to Luke and Leia, his dynamic with Obi-Wan was arguably more interesting. They did have major disagreements, but they also shared a lot of great moments together, solidifying their friendship.
Obi-Wan had been with Anakin throughout his journey. Initially, Qui-Gon Jinn was supposed to train the young boy from Tatooine, who he was convinced was the Chosen One, even when the Jedi Council objected. This was the reason why even on his deathbed, he was adamant Obi-Wan take over Anakin's training, as the Jedi Council may not have continued it themselves if Anakin didn't have a master and advocate in Qui-Gon's absense.
Marvel's Obi-Wan & Anakin mini-series revealed this ultimately became a problem for Anakin, as one of the lack of trust and advocacy from the Jedi Council and the rest of the Jedi Order, in general, was a major source of frustration. He didn't only feel like an outsider to the Jedi, but also as if the Order was holding him back from his true potential to help the galaxy, so during his early days of training with Obi-Wan, he almost quit. While Obi-Wan had never known life outside the Jedi Order, he was fully ready to follow him if he moved forward with his decision.
In a conversation with Yoda, Obi-Wan revealed that no matter what happened, he planned to keep the promise he made to his own mentor, Qui-Gon, whose last imperative was to ensure that Anakin is trained. Interestingly, Qui-Gon didn't specify that Anakin must be trained as a Jedi, simply that he "must be trained" so he could fulfill his destiny as the Chosen One.
Obviously, Anakin eventually changed his mind and stayed, but it's curious to know how things would've turned out if both of them left the Jedi Order, but continue to train in the Force. There's a possibility that, free of the Dogma of the Jedi, they may have become the last vestige of protection against the Sith's secret rise. Seeing Anakin walk away from the Jedi would also mean that Palpatine would've had a more difficult time getting access to him. Instead, the Padawan would spend more time with Obi-Wan instead, who would most likely keep him on a straight path, possibly even forming their own new order of Force users more true to the true ideals of the Jedi, not like the corrupted Jedi Order shown in the prequels.
While Obi-Wan's decision to follow Anakin if he did leave the Jedi Order mostly stemmed from his promise to Qui-Gon, it also highlights how invested he was in his Padawan. This makes their falling out a lot more painful than just seeing their fight in Mustafar. In any case, what's clear is Obi-Wan remained committed to Anakin as he devoted his life to ensuring that Luke was safe.