How did Obi-Wan so easily defeat Anakin?

Obi-wan pleads Anakin not to jump. His exact words are somewhat like these "Do not try Anakin! I have the higher ground." Means he was pretty sure he would win if Anakin made that jump. Also, let us assume Anakin tried to jump to the side. But by that time Obi-wan would also have reached there and delivered an equally fatal blow. After all, he is a Jedi Master too and he is the one who mentored Anakin.

Obi-Wan Kenobi is a Master Jedi*

He is a diplomat first and foremost but he is also one of the greatest strategists the Jedi order had at the time period. Despite his preference for diplomacy, Master Kenobi was known as one of the greatest swordsmen the order had ever seen, and the definitive master of Form III (Soresu) lightsaber combat. In his early years, Kenobi had become very skilled with Form IV: (Ataru), but later abandoned it because of its lack of defense that resulted in the death of his master, Qui-Gon Jinn. Kenobi also knew elements of the Form VIII (Sokan).

Along with Kenobi's lightsaber mastery, he was very advanced in the art of mind trick and force persuasion. He had learned from the spirit of Qui-Gon Jinn the ability to become a Force ghost, something he later used to guide and counsel Luke Skywalker

Knowing all this it is not hard to presume that Obi manoeuvred Anakin to a no win position where he then could apprehend him. In the movie he doesn't want to kill Anakin. Kenobi pleads with Anakin to stop, but Anakin is too far gone to the rage and his only goal is to kill Kenobi. All other objectives are a distant secondary.

That is why he cant see past the next move he has to make. Obi Wan is detached, fights defensively as that is his preferred mode of attack. He waits, bides his time and watches for a mistake. At the end Anakin has put himself in a bad position but because of his rage and single minded desire to kill Obi-Wan he fails to plan ahead and that is why he looses.

• Most of that is compilation from other sites, wiki pages and cannon sources.

I do agree with other posts in the sense that Obi-Wan was a master of form III, which was said to directly counter Anakin. I have an additional point though which I believe explains the way the movies play out.

I think what is lost here is that through the course of the fight, we see a parallel between the two fighting styles. The fact that the two use force push at the exact same time is evidence of this (although the freeze frame looks silly here):

You see many sequences where the two follow the same sequence of attacks if you watch closely. That explains the stalemate for much of the fight. The two knew each other so well that they could predict each others attacks.

Towards the conclusion of the fight, we see Anakin somewhat taunt Obi-Wan when he is ready to finish him:

Anakin Skywalker: [raises his lightsaber] This is the end for you... my former master.

And I think we see that when Obi-Wan escapes even after Anakin made his victory claim immediately angers and enrages him:

After this, Anakin goes on tilt and makes a mistake (ask any MOBA player what that is like) and the fight is lost.

In conclusion, I believe the movies show us that the duel between Anakin and Obi-Wan is nearly a complete stalemate. When Anakin could not break the defense of the Form III he becomes frustrated and fatigued (remember its really really hot on Mustafar) and he acts outside of his training and knowledge, leaving himself vulnerable and costing him the battle. This is the perfect reason why Form III is so strong on a Jedi and why the fight in the end goes to Obi-Wan.

Also, the goal of many Soresu practitioners was to prolong the fight, the idea being to cause the enemy to become fatigued or frustrated as they attempted to keep up their offense.[4] However, this tactic ran the risk of fatiguing the user if said user was to face an adversary who could maintain an aggressive but cautious offense.[15] - Wookieepedia on Form III

Obiwan jumped to high ground because he was facing defeat you can tell by the look on his face before he jumps

It was very evenly matched but dont forget obiwan jumped of that platform for a reason and he was fortunate to gain the high ground in fact

had that fight been in arena style, anakin would have won easily, he was the aggressor throughout the fight and was backing up obi-wan the whole time. anakin just made one stupid mistake. a fight i would have loved to see would be anakin vs mace windu.

Dooku was a sith, not a master of Form 3, and not overtaken with the rage, (hence his brown eyes). Many circumstances go into battle, and Obi-Wan had all the aspects in his favor to fight an angry Anakin.

Anakin Skywalker had a "habit" of losing his light saber. "This weapon is your life!" Obi-wan would tell Anakin. This was made fact in previous Star Wars films. At the end of the fight on Mustufar, Anakin made his leap to confront Obi-wan and he lost his light saber. Anakin's legs and left arm was severed from Obi-wan's light saber slash but his right arm was intact.

Anakin lost because he was still using the Jedi Lightsaber he created while still being a lightside force user. Had he been using a darkside force meditated lightsaber Anakin would have beaten Obi Wan. Anakin was then at a disadvantage using the blue saber and Obi Wan could possibly be advantaged by the Jedi weapon and could possibly predict Anakins movements.