WARNING: The following contains major spoilers for "A Distant Echo," the latest episode of Star Wars: The Clone Wars Season 7.
There was no one thing that led to the fall of the Jedi Order and the rise of the Empire in Star Wars. The Jedi's failures came from hubris, as the organization believed itself too powerful to fall and ignored all the signs that were so clear to anyone who paid attention. For Anakin Skywalker, the man who would become Darth Vader, his failings stemmed from his passion.
While most would say it was anger that led to Anakin's turn to the Dark Side, the truth is it was love that caused his fall, more specifically his secret marriage to Padme Amidala. Revenge of the Sith hinted Obi-Wan Kenobi knew of Anakin and Padme's relationship. However, his knowledge wasn't confirmed until the most recent episode of Star Wars: The Clone Wars, "A Distant Echo." And now, knowing Obi-Wan was aware of the romance between Anakin and Padme, it's hard to ignore the Master Jedi's role in the fall of the Galactic Republic.
Keeping Anakin and Padme's relationship a secret isn't Obi-Wan's only mistake the Clone Wars has brought to light, but it is the most serious. He knows his closest friend, a man he considers his brother, is deliberately breaking Jedi law and allowing his emotions to control his actions. This, of course, puts Obi-Wan in a precarious position: Should he have reported what he knows to the Jedi Council, likely leading to Anakin's expulsion, or should he, for lack of a better term, keep to the bro code? While it's clear Obi-Wan not telling the Council what he knew would, in part, lead to their destruction, there was no way for the Jedi Master to know that himself.
Still, Obi-Wan does know Anakin is one to let his emotions get the better of him, which had led to more than a few poor decisions on Skywalker's part. And as someone who was himself in love with Duchess Satine Kryze of Mandalore -- though he never acted on his feelings -- Obi-Wan understands how the emotion can overpower everything else in a person's mind. By not reporting what he knew to the Jedi Council, Obi-Wan let his emotions make the decision for him. It is his love for Anakin that Obi-Wan is acting on.
At the same time, Obi-Wan may have a logical reason not to tell the Council. Anakin is one of the best generals in the Clone Wars, and to lose him at the height of the war, when the Separatists are seeming to attack with more ferocity, could well cost the Galactic Federation the war. This isn't hyperbole, either. More than any other crew, Obi-Wan and Anakin are the ones the Jedi Council and the Republic depend on for the major battles.
Obi-Wan likely also considered that Anakin relies too much on his emotions, and being tossed out of the Jedi Order, something he has been a part of since he was a child, probably isn't something his pupil would take in stride. A push like that could have put Anakin down a dangerous path, leading him to the Dark Side. From Obi-Wan's point of view, Anakin may have been breaking Jedi law, but at least he was still with the Order. But when breaking down all the factors: Obi-Wan's greatest failure was not confiding in Anakin.
Obi-Wan's relationships with Duchess Satine, much like the romance of Anakin and Padme, also ended in tragedy. Obi-Wan held to his Jedi code and never acted on his feelings for the Duchess, but his love for her was powerful enough Darth Maul could sense it. When Maul invaded Mandalore, he held the Duchess captive and waited for Obi-Wan to arrive. In front of Obi-Wan, Darth Maul murdered Satine, giving the Jedi Master a first-hand experience of what Darth Sidious would later use to turn Anakin.
Knowing Anakin was in love, Obi-Wan should have opened up to his Padawan and shared his own story. Together, the two Jedi could have talked about their feelings, and how to best handle them. Even more, Anakin wouldn't have felt so alone and in need of someone to talk to. Instead of turning to Palpatine, he could have confided in his closest friend and mentor.