It's not really about insight. I mean, therapy will usually bring insights, but insights do not necessarily bring change.
Discovering a truth is sometimes an early step. For instance, you might arrive fairly easily at the insight that you grew up feeling that your father was a competitor, and that this has hurt your career. Knowing this intellectually is different from really feeling its truth. Feeling its truth is different from accepting it. And accepting it is different from taking responsibility for the choices you made as this unfortunate dynamic played out.
Sometimes change in therapy can occur without much insight. For example, someone who is very reluctant to acknowledge or express anger may be able to work out this constriction in his or her relationship with the therapist. Therapy is a place you get to have all your thoughts and feelings. Pissed off about all the money you're paying the idiot sitting silently across from you? Part of your responsibility in therapy is to make sure the idiot knows how you feel. Therapy is the one place where you can say what you really think and how you really feel without repercussions.