Group 7 elements would want to gain a full outer shell, but would they do it in the same way, as in lose them all?
Elements in Group 7 don't want to lose 7 electrons. they would want to gain an extra electron...
it's easier.
Thus, to gain an electron, they would want a larger nuclear force, which is where there are less electron shells for shielding.
Therefore, reactivity is higher when ther are less electron shells, ie. fluorine.