The problem with Obi-wan’s speech is that it’s simple enough without ESB and ROTJ:
Obi-wan had at least two students, one of which was later known as Darth Vader, betraying and murdering Anakin. Simple, effective, and good motivation for Luke to become a Jedi.
Actually, if you go only by the original Star Wars, Luke’s father was never established as Obi-Wan’s student. Only Vader was. Anakin was merely ‘a good friend’. Only after the two characters merged in ESB, Anakin is soft-retconned into being Obi-Wan’s apprentice.
Once again I would like to put forward the idea of dismissing the official master-apprentice relationship altogether. Anakin spends some time with Obi-Wan and is taught about the Force. Does that make him Obi-Wan’s apprentice? Perhaps it does, perhaps it doesn’t. This way when Ben later refers to his apprentice, he may very well be talking about Anakin, or maybe some proper student he gets involved with some time later. It works either way.