There are two ways to approach your question: 1) To pretend the prequels don't exist; 2) to answer your question based on the events depicted in the prequels.
1) is relatively straightforward. You can imagine a really dramatic and psychologically complex relationship in which Obi Wan failed his friend in some important way; or
2) There is actually dialogue in the duel that addresses this issue somewhat. When Ani and Obi are floating around on the lava-capture droids in the Ep III duel, Ani says something (I forget what) and Obi says: "I have failed you, Anakin." I interpreted this as Obi-Wan blaming himself for his failure to properly instruct, indoctrinate, and mentor Anakin.