does"break it to him" mean "she won't tell the new to Robert,"or "she didn't believe the news?"
On the fifth floor of the Justice Department Building at Ninth Street and Pennsylvania Avenue, J. Edgar Hoover had picked up his direct line to the Attorney General's office. It was answered by Angie Novello, who was staring across a desk at a frayed UPI page held aloft by a weeping press office secretary.

"This is J. Edgar Hoover." His delivery, as always, was staccato, shrill, mechanical. "Have you heard the news?"
"Yes, Mr. Hoover, but I'm not going to break it to him."
"The President has been shot. I’ll call him."

Question

does"break it to him" mean "she won't tell the new to Robert,"or "she didn't believe the news?"
On the fifth floor of the Justice Department Building at Ninth Street and Pennsylvania Avenue, J. Edgar Hoover had picked up his direct line to the Attorney General's office. It was answered by Angie Novello, who was staring across a desk at a frayed UPI page held aloft by a weeping press office secretary.

"This is J. Edgar Hoover." His delivery, as always, was staccato, shrill, mechanical. "Have you heard the news?"
"Yes, Mr. Hoover, but I'm not going to break it to him."
"The President has been shot. I’ll call him."

Answer

It means, she is not going tell Robert the news.

Answer

to break it/the news to somebody:

to tell someone about something unpleasant that will affect or upset them:

- Come on, what happened? Break it to me gently (= in a kind way).
- I didn't want to be the one to break the news to him

[http://dictionary.cambridge.org/dictionary/british/break-it-the-news-to-sb]

We also have 'breaking news', which is news which has happened very recently. The 'breaking' part, is the telling someone who didn't know.

집에서 편안하게 언어를 배울 수 있는 기회를 놓치지 마세요. 경험 많은 강사진을 살펴보고 지금 바로 첫 수업을 신청하세요!