In the last battle of Episode 3, Obi-wan tells Anakin not to try jumping at him. Why does he do this? If Anakin surrenders, Obi-wan can't take him into custody and put him on trial, since the Republic has fallen. I wondered if Obi-wan was actually trying to goad Anakin into making that ill-advised jump, but he seems sincere when he says "don't try it". What does Obi-wan want Anakin to do at this point?
He actually likes Anakin and doesn't want to kill him.
A Jedi that is not fueled by hate would not make that jump since it's obviously a bad idea, whereas a Sith lets his rage guide him into making that jump.
If he would have surrendered I guess Obi-wan would have given him another chance to come to the light side, so with 1. he hopes that that's the outcome.
Hope that's kinda understandable.
Apart from the in-universe factual explanation, there is also the metaphorical necessity. In that scene, Obi-Wan temporarily got the "high ground", an important tactical advantage for fencing. By showing a reluctance to kill Anakin, and offering him a chance at redemption, Obi-Wan takes the moral high ground as well. Obi-Wan is the last white knight; he must be gallant to the last.
One may argue that being a jedi knight implies such poses. Possibly, Obi-Wan feels compelled by the Force to do so; not offering that last chance to Anakin would constitute a step in the direction of the dark side. But, also, this over-the-top display of chivalry is constitutive to the story as a whole; it makes it worth telling.
In that sense, it is similar to the business between Luke, Vader and the Emperor at the end of Episode VI: while they were sword-fighting, the murder-bears were mincing through the imperial troops, and the second Dark Star would have been destroyed regardless of whether Luke had won or had succumbed to the dark side. But in the Star Wars universe, everything happens both factually and spiritually. This is a fundamental principle of how things work in that far, far away galaxy. Without this mirroring between metaphors and tangible events, Star Wars would be a mere accumulation of peripeties; it would look like a Star Trek episode (with a bigger budget).