I actually passed the breath test, but the police still arrested me. How is that possible?

You can be charged in Florida under two theories. Either an unlawful blood alcohol level, or driving under the influence, which is based on whether or not you have use of your faculties. So an officer can charge you based on his observations, his mere opinions, that you are impaired. That would be a decision that a jury or a judge would have to make the ultimate determination based on those faculties, what the officer observed, whether or not you are impaired to the point of being DUI.