I'm not sure I can explain anything related to the FDA (I'm European) but maybe I can shed some light on the insight what people are worried about.
These vaccines have been applied hundreds of million times in the past year, true. Therefore, we have a very good understanding of their adverse effects in the first 6-12 months. What we cannot know, however, are possible adverse effects that are longer term. Susceptibility to other diseases maybe due to a weakened immune system. Possibly a higher prevalence of autoimmune diseases.
If these vaccines were regular, inactivated virus vaccines, we could extrapolate long term effects from other similar vaccines. But this is brand new technology which affects our immune system, which is far from completely understood.
These vaccines have been applied hundreds of million times in the past year, true. Therefore, we have a very good understanding of their adverse effects in the first 6-12 months. What we cannot know, however, are possible adverse effects that are longer term. Susceptibility to other diseases maybe due to a weakened immune system. Possibly a higher prevalence of autoimmune diseases.
If these vaccines were regular, inactivated virus vaccines, we could extrapolate long term effects from other similar vaccines. But this is brand new technology which affects our immune system, which is far from completely understood.