Anakin’s lava-filled duel with Obi-Wan Kenobi on Mustafar is one of the best and most consequential duels in all of Star Wars. The climactic moment in Revenge of the Sith pushed both characters to the edge of their abilities as they fought for everything that they held dear. They were brothers, but Anakin’s murderous actions against the Jedi had forever alienated him from his former master. He had become what he had sworn to destroy – a Sith.
There have always been debates among Star Wars fans as to why someone of Anakin’s abilities – in the Force and with a lightsaber – lost to someone like Obi-Wan, and most of the answers are fairly similar. They claim that Anakin was so prideful that he wanted to best his master at his own game by trying to flip over him like Obi-Wan flipped over Darth Maul. Ultimately, he failed and became the monstrosity that was Darth Vader. That may not be the only reason that Anakin lost, though, because it seems that Anakin never actually used the Dark Side during their duel.
When a Sith is using the Dark Side, they must give in to anger, violence and a will to dominate. It’s what the Sith code calls for, and one of the best ways to see if a Sith is successfully tapping into darkness and wrath is through the color of their eyes. Star Wars: The Visual Encyclopedia says that "as windows to the soul, eyes reflect the emotions harnessed by the Sith. When rage and anger seethe inside a dark side user, their eyes may burn yellow with a fiery-red rim."
Just before the fateful duel, Anakin was on Mustafar to execute all of the Separatist leaders, and during that scene, his eyes blazed yellow with a vengeance. All of his pent-up anger from years of fighting in the Clone Wars came out as he massacred them. He had no reason to hold back because he was carrying out the will of his master and fulfilling his own desires. So, his rage was reflected in his eyes as he butchered the helpless leaders. When Padmé arrived, things changed. As twisted as his actions were, he was doing everything for her. At the sight of his loved one, he no longer had a reason to be angry, and his eyes returned to normal.
Then he saw Obi-Wan. He was specifically mad at his previous master for asking him to spy on the chancellor, declining him the role of Jedi Master and “stealing” Padme from him. Going by the Visual Encyclopedia's rules, Anakin’s eyes should have turned yellow with a vengeance, but they did not. They remained normal for the entirety of their duel, which seems rather odd. While a Sith can use the Dark Side without their eyes turning yellow, it’s only possible if anger is curtailed while doing so, like in the case of Count Dooku. Anakin was certainly angry, so if he was using the Dark Side, his eyes should have undoubtedly been yellow.
All of this appears to indicate that Anakin didn’t use the Dark Side while fighting his former master. While the high ground was important, the real reason he lost to Obi-Wan might have been because he never unlocked his true potential in the Dark Side during their duel. Obi-Wan was an extremely tactful and strategic duelist, but that shouldn’t have mattered. As one of the most powerful Jedi in Star Wars, Anakin's potential was unlimited, even beating the legendary duelist, Count Dooku. Since he beat Dooku while using the Dark Side, Anakin should have been able to take Obi-Wan down with relative ease because Dooku was a much better swordsman than Obi-Wan.
This then begs the question of why Anakin was not using the Dark Side during this duel, and there are two possible answers. The first is that, deep down, Anakin knew that he was wrong. He had just destroyed everything he had ever stood for, killing Jedi and slaughtering younglings. His eyes were not yellow during the sacking of the Jedi Temple because, as a newly christened Vader, the event was meant to callous his heart. Thus, as mad as he thought he was at Obi-Wan, perhaps he couldn’t quite bring himself to fully embrace the hate of the Dark Side until he lost the duel.
The second option as to why Anakin did not use the Dark Side is his pride. Anakin had spent his entire Jedi career trying to prove his worth and power to everyone. As Star Wars' resident Chosen One, he had immense pressure on him, and some people were always critical of his progress. So, when Obi-Wan arrived to challenge him, it’s possible that he wanted to prove to his master that he was the more powerful Jedi once and for all. He thought that he didn’t even need the Dark Side to beat Obi-Wan, but he was wrong. When Anakin became overly ambitious, Obi-Wan struck and ended the duel, allowing Anakin to fully embrace his hate and become the armor-bound Darth Vader.