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?
It is psychology.
It is quite clear from the dialogs, that Luke probably idolizes his father, as he jumps right away when his father is mentioned in any way, because he represents something that he dreams of.
Obi-wan knows this, and tells this lie to Luke to motivate him, to manipulate him. Obi-wan wants him to believe that he can actually do something, that his father always wanted him to do.
If he’d say what you suggest, that “by the way, I have your father’s lightsaber, if you want it.”, it would only mean that he gets an object, that he can put in a drawer, and Obi-wan would not get the result he wants.