Exclusive: Tim Cook Not Budging on Apple Privacy Decision: 'Safety of the Public Is Incredibly Important' He told ABC News' David Muir why he would not break into Syed Farook's iPhone.

 -- In an exclusive interview today, Apple CEO Tim Cook explained to ABC News anchor David Muir why he refused to create software that would help the FBI break into an iPhone used by one of the San Bernardino, California, shooters.

"I think safety of the public is incredibly important -- safety of our kids, safety of our family is very important," Cook said. "The protection of people's data is incredibly important, and so the trade-off here is we know that doing this could expose people to incredible vulnerabilities."

The interview will air today on "World News Tonight with David Muir" at 6:30 p.m. ET and on "Nightline" at 12:35 a.m. The extended interview will be available online at ABCNews.com immediately after "World News Tonight."

The FBI has called on Apple to help crack into the iPhone of Syed Farook, who, along with wife Tashfeen Malik, killed 14 and injured 22 at a holiday party in December. Last week, at the request of the Justice Department, a federal judge ordered Apple to assist law enforcement. The tech giant, however, refused and vowed to fight the order, sparking a continuing fight between federal authorities and Silicon Valley.

"This [master key] is not something we would create," Cook said. "This would be bad for America. It would also set a precedent that I believe many people in America would be offended by."

When asked whether he had any concerns that he might be able to prevent a terrorist attack by breaking into Farook's iPhone, Cook said: "David, some things are hard and some things are right. And some things are both. This is one of those things."