This woman indicated she had pursued her husband's self-disclosure, but he was resistant. She wisely noted that she did not want him to see her as critical or nagging.
I think the best way to "bring out" a man is by being vulnerable with your feelings, saying, "I feel distant or I feel lonely even when you are close." If he says he doesn't care how you feel, then you've got a bigger problem than communication. If he cares, he will try to figure out how to repair the chasm between you.
Being vulnerable means that your tone is soft, without a hint of aggression. Being vulnerable also means that you are sharing your view and your feelings, not describing his failure to communicate.
Despite being vulnerable, some men will still respond defensively. It is important to respond, "I'm sorry you feel attacked, what is it I said that caused you to feel I was criticizing you?" After he sites the implied criticism, you can redirect him to your feelings. Keep the focus on your feelings and your desire for him to respond out of caring, not pressure to perform.