Take a hypothetical disease A that started spreading on Jan 1st. It takes a patient 1 month to recover from A, while it only takes 7 days for A to kill. We perform a calculation on Feb 9th to determine A's case fatality rate.

The correct way to calculate A's case fatality rate would be to select a cohort, Group B, for example: everyone infected in the first week. And calculate:

(deaths in Group B by Feb 9th) / (deaths in Group B by Feb 9th + recovered in Group B by Feb 9th)

An incorrect way to calculate A's case fatality rate would be:

(deaths by Feb 9th) / (deaths by Feb 9th + recovered by Feb 9th)

This is incorrect because "deaths by Feb 9th" includes all deaths from people infected between Jan 1st and Feb 2nd, while "recovered by Feb 9th" only counts the recovered patients who were infected between Jan 1st and Jan 9th. The above equation basically expands to:

(deaths in Group C by Feb 9th) / (deaths in Group C by Feb 9th + recovered in Group D by Feb 9th)

Where:

Group C: infected between Jan 1st and Feb 2nd

Group D: infected between Jan 1st and Jan 9th

Since disease A is spreading exponentially, it's clear that Group C is a few orders of magnitude larger than Group D.