At the meeting, Mr. Zuckerberg asked Mr. Cook how he would handle the fallout from the controversy, people with knowledge of the conversation said. By urging Facebook to stop gathering that information, Mr. Cook was in effect telling Mr. Zuckerberg that his business was untenable. Two years later, Mr. Zuckerberg and Mr. Cook’s opposing positions have exploded into an all-out war. Mr. Zuckerberg, 36, is a Harvard dropout who built a social-media empire with an anything-goes stance toward free speech. While Mr. Zuckerberg once took walks and dined with Steve Jobs, Apple’s late co-founder, he does not do so with Mr. Cook.