inorganic chemistry - Why is fluorine the best oxidising agent, but also the most basic?

(Please note that all comparisons I have made below are with respect to halide ions only.)

According to what I have learnt, the fluoride ion is the most basic ion, because it has the smallest size and thus the highest electron density. This implies that it has the highest tendency of sharing/giving away its electron density.

Why isn't the same logic applicable when reducing strength is compared? Fluorine should have the highest tendency to lose electrons, and hence should be the best reducing agent.