A Star Wars theory surrounding Star Wars: The Rise of Skywalker could explain the real reason why Leia did not become a fully-fledged Jedi. In the film, it was established that Leia once trained under her brother Luke to become a Jedi. The training even went far enough that Leia crafted her own lightsaber, though eventually, she decided to abandon the path of the Jedi and become involved in New Republic politics.
As is known from the Star Wars sequel trilogy, Leia's Force powers were inherited by her son, Ben Solo. Ben then went on to train with Luke, with The Rise of Skywalker explaining why Leia chose to abandon her training, leaving the ways of the Jedi to Ben. This explanation has spawned a dark theory, that could uncover the true meaning behind why Leia did not continue to train as a Jedi in a tragic turn of events, despite Leia potentially being a stronger Jedi than Yoda.