Health leaders and politicians entire job is to build and maintain trust. Mistakes like this only reinforce vaccine hesitancy. Those that are hesitant know that the science is settled - until it isn't. The only method to account for unknown unknowns is time.

It would have been entirely possible for Fauci et. al to say "The vaccine data appears to show 95%+ efficacy, but we will be waiting to lift lockdown mandates be sure". That kind of messaging shows both a respect for science and a commitment to everyone's health. However, it was an unpopular political decision, so mandates were lifted.

This isn't the first time they've changed their course after making a decision prematurely. To the vaccine hesitant, why is this FDA approval any different? There's massive political pressure to approve these vaccines.