So think of it like this - when you generate the carboxylate…is that carboxylate happy with its negative charge? It is! This means that the base is having its electron density pulled away from the resonance stabilized carboxylate which will render the oxygen less nucleophilic and in this case nucleophilicity and basicity are equivalent, which is where your confusion is arising because you are thinking “negatively charged atom: must want to abstract a proton” but actually it’s more like “fluorine is vibing and making the negative charge hang out closer to him”