Obi-Wan tells Luke “your father wanted you to have [the lightsaber] when you were old enough.” He also mentions Owen being afraid Luke would follow Obi-Wan on some “idealistic crusade” like Anakin.
This one bugs me because you can’t really justify it as Obi-Wan simply lying about Luke’s father. Why even bring it up? All he needed to say is “by the way, I have your father’s lightsaber, if you want it.” Why even mention anything about the “idealistic crusade” or Anakin wanting Luke to have the lightsaber? AotC shows us Owen and Anakin interacting for maybe a day. Prequel Owen clearly wouldn’t have any reason to care that Anakin left to go save Obi-Wan from the termites. Everything in the original scene points to a backstory where Owen and Anakin grew up together, and Owen was upset when Anakin left with Obi-Wan to go fight in the war.