Why is fluorine more reactive than chlorine despite lower electron affinity?

It does seem contradictory, but reactivity depends on more than electron affinity. Fluorine is small, so when an extra electron approaches its compact 2p subshell, there is strong electron-electron repulsion in the tiny shell. This repulsion makes fluorine's electron affinity slightly lower than chlorine's. However, reactivity is governed by the overall ease of reaction. Fluorine has a very low bond dissociation energy for F-F (the bond is weak because the small atoms' lone pairs repel), so the F2 molecule splits apart easily. It also forms very strong bonds with other elements, releasing a lot of energy. Combined with its high electronegativity and small size, these factors make fluorine the most reactive non-metal even though its electron affinity is a touch lower than chlorine's. NEET often tests this exact anomaly.