Why are rockets launched from Florida?

There are several main reasons that Cape Canaveral was chosen for NASA's main launch center when it was created in 1958, but the biggest reason is the most obvious; Location, Location, Location.

Most people don't realize it, but Kennedy Space Center is only part of a much larger complex. Cape Canaveral Air Force Station (Patrick AFB), across the Merritt Island Causeway from KSC, was there before NASA was created, was in a remote location (then) and provided the military security required to conduct classified missions and work. As a result, when NASA was created, it was a prime spot and was chosen for NASA's launch facilities.

Additionally, besides its remote location, by virtue of being next to the ocean, it provides all launch vehicles with a safety factor not available with launch locations (e.g., Vandenberg AFB) deeper inside the United States. All launches have a downrange trajectory over the Atlantic Ocean (usually East, but occasionally North up the East Coast of the U.S. if required) so that in the event of an accident or the need to intentionally destroy a launch vehicle, any collateral ground damage will be minimal.