“In training, her potential rivaled my own. Leia told me her fate was bound to the core of galactic affairs, not the rigid path of a Jedi. She surrendered her saber to me…”

I’m willing to re-word this one, but I think it accomplishes three different things.

Leia is possibly even stronger with the Force naturally than Luke (thus why she beats him).
She senses that she needs to play a more active role in the galaxy than what the Jedi would allow.
Luke trained Leia for an indeterminate amount of time so that everybody is happy around here.