Hurricanes that threaten the United States start their lives over the Sahara desert in Africa. They move out over the Atlantic Ocean to build into tropical storms and then hurricanes. While they are over the Atlantic near the equator, hurricanes are pushed toward the U.S. by trade winds. Trade winds are very consistent westward winds near the equator.
Once the storm rises up toward 25 or 30 degrees latitude (the top of Florida is at latitude 30 degrees), the trade winds are no longer a factor, and local weather over the United States has a big influence. Winds along the East Coast tend to blow in a north or northeast direction, and there is also the eastward-blowing jet stream. These winds often cause a storm that comes in from the west and appears to track right up the East Coast, or to approach the East Coast and then back off. Any number of fronts or pressure zones may be in place over the U.S. as the hurricane comes in, and these systems have their own winds that can significantly influence a hurricane as well. If a storm tracks from the west and does not get far enough north to lose the effect of the trade winds, it will instead continue westward into the Gulf of Mexico with the trade winds and land in Texas or Mexico.