They spun a web for me...
Obi-Wan knows it would be merciful to kill Anakin, but he also realizes that it would endanger him to climb any further down the embankment (fire, lava...bad idea), and he also realizes that at that moment, the only way to save the man that he knew and loved as Anakin Skywalker is to try and get Padme and their children to safety. He has to quickly weigh the consequences in his mind, and the only thing he feels he can do is leave Anakin and return to the hangar to get Padme off of Mustafar and to a medical treatment center. I also think that at this particular point, Anakin is completely swallowed up by the Dark Side and the persona of Darth Vader, and Obi-Wan can sense that. Anakin Skywalker does not return until many years later, when he is faced with his son, and it is that spark of love that proves to be his salvation. Had Obi-Wan not left him on that embankment, then he would have died a Sith, or the twins would have been lost and the Dark Side truly would have conquered. Obi-Wan had to leave him to continue the fulfillment of Anakin's (and the entire Skywalker) destiny.
"I will miss our conversations..."