Fluorine is a highly reactive gas, so is chlorine for that matter. Fluorine is also capable of supporting combustion, much like oxygen. Fluorine is a small atom with a tremendous ability to attract and share pairs of electrons, thus forming bonds.
The electron affinity is the energy given off when one electron is added to a neutral, gaseous atom. Fluorine is such a small atom, with a high electron density in its outer-most level, so much so that there is more repulsion in forming a -1 charged atom than there is for chlorine.