[Writer's Option] elaborate: with or without "on"

[simile]

In Oxford dictionary, it says:
He said he was resigning but did not elaborate on his reasons.
She went on to elaborate her argument.


"elaborate on his reasons" and "elaborate her argument" both exist.
How do I interpret the use of "on"?
Does that mean the use of the preposition is the writer's option?
Either one is good. And there's no difference?

[SlickVic9000]

(Not a Teacher)

They mean the same thing to me.