The topic came up yet again on Monday night at the Wall Street Journal’s technology conference in Laguna Beach, Calif. where Apple CEO Tim Cook followed NSA director Admiral Michael Rogers on stage. They shared contrasting views about a number of hot button issues around privacy, which have created a deep divide between Silicon Valley and the nation’s security apparatus.

Should companies give authorities “backdoors,” or easy access to their user data to investigate national security cases? And should companies be allowed to encrypt user data so that agencies that do gain access see only gibberish?

“We’ve said that no backdoor is a must, and we’ve said that encryption is a must,” Cook said after being asked about his privacy stance.

“You’re saying, ‘They’re good, so it’s okay for them to know,'” he added about the government’s argument. “But that’s not the state of today. If someone can get into data, it is subject to great abuse.”

The federal government routinely asks large companies like Apple (AAPL) for user data and cooperation in national security investigations. Documents leaked by Snowden showed that the National Security Agency went much further by vacuuming up huge troves of email and other digital data.

Tech companies, fearful of users defecting from their services, started fighting back. Many started tightening their security to circumvent government snooping.

Cook’s sensitivity on the subject likely goes back to 2013, when Apple was accused of working with the NSA to provide backdoor access to its customers through hidden software on its iPhone handsets. Apple quickly denied allegations of ever working with the NSA and has since pushed a pro privacy message, even winning praise from Snowden for a pledge to never sell consumer data.

The NSA’s Rogers argued that all parties involved should find a way for the agency to collect intelligence that keeps everyone safe — and to do so within boundaries the country, as a whole, is comfortable with.

“Strong encryption is in our nation’s best interest,” he said, before quickly clarifying he means strong, not full encryption of email and online files. The nuance is that strong encryption would still give his agency access to user information while full encryption would make the data unreadable.

Rogers spent a great deal of time encouraging greater collaboration between Washington, D.C. and Silicon Valley in developing better technology and strengthening online security. He also claimed that Snowden’s document leaks have affected the NSA’s effectiveness to protect the country.

“We can’t do that in a world in which both sides castigate each other, ‘I’m good, you’re bad,’” he said.

But Cook’s stance was clear. When probed by Wall Street Journal editor-in-chief Gerard Baker on whether a compromise could be reached, Cook interrupted:

“You’re making an assumption, I think you’re going off the deep end with your assumption… I think it’s not so simple. Gerry, I think we would all agree that if there was a way to expose only bad people, whoever the determiner of what bad is, that would be a great thing. But this is not the world.”

He continued: “You may not agree with that, but today, I don’t know a way to protect people without encrypting.”

Still, the only point both Rogers and Cook could agree on, is that neither security nor privacy should be compromised. “No one should have to decide, privacy or security, we should be smart enough to do both,” Cook said.

Unfortunately, neither gentleman could offer a solution.

Subscribe to Data Sheet, Fortune’s daily newsletter on the business of technology.

For more on some of Apple’s others security woes, watch this Fortune video: