His wish was finally fulfilled ever since he was a Jedi as Anakin Skywalker but was rejected by Windu and the rest, Palpatine now gave him his wish and it was ruthless.

Obi-Wan spent the last 20 years living in the middle of nowhere while Vader was conducting a witch-hunt on remaining Jedi and the Rebellion. He believed he was now equal to or more accomplished than his old master. And Darth Vader is too confident a man to claim himself apprentice to Sidious.

Another possibility is that this is one of those things that makes Episode IV a bit odd. When it was released I don’t think there was anything to indicate the Emperor was a dark wizard or that Vader was anything closer than his right-hand enforcer (recall that Leia’s commentary suggested Vader was working subordinate to Tarkin like some choke-happy attack dog). There was a mention of him among the council of moffs but all we gathered was doubt this unseen man could control things without the senate.