BF3 Lewis Config and Octet Rule?

The formal charge, if you were to draw a double bond from a Boron atom to a Fluorine atom, would leave the Boron atom with a more negative charge than the Fluorine atom. This would be an incorrect Lewis Structure if the less electronegative atom has a more positive charge than the MOST electronegative atom on the periodic table. Sorry if I misunderstood something, it's been a while since I've fooled with Chem, but I believe that is why.