tl;dr: (I love the New Yorker most of the time, but their bury-the-reader-in-prose style is absolutely NOT an appropriate fit for this story)

1. A technical messup led to the orginal batch of CDC tests being bad. This seems unavoidable. Stuff happens.

2. A bureaucratic disaster in HHS led to delays trying to get private tests certified. This will forever be fodder for conspiracy arguments, as both the HHS secretary and president were issuing statements at the time pointing to low positive test counts as evidence for the virus not being serious.