In the spirit of the principle of charity, it isn't that hard to believe that part of the discussion is the impact the virus will have on classified activities, including but not limited to intelligence activities, military activities, or may have included information considered sensitive (like, just by way of example, proof that the virus was gene engineered, which may cause an undesirable international stink if publicized; I mention this just as an example of something that they might classify, not as a claim that it is engineered).

I'd expect "the President" did not literally decide or not decide to classify this; it was probably driven by rules.

What's in the classified briefings isn't really the question; it's what's in the unclassified briefings and actions that are the question. That classified briefings are taking place is to be expected, as it will certainly be impacting classified things, along with all the other "pretty much everything" it will be impacting. I'm sure all the other countries are having classified briefings as well.