From Wikipedia:
... the Council of Trent authorized Pope Paul III to reform the calendar, requiring that the date of the vernal equinox be restored to that which it held at the time of the First Council of Nicaea in 325 ...
At the time of Gregory's reform there had already been a drift of 10 days since the Council of Nicaea ...
Lilius's formula was a 10-day correction to revert the drift since the Council of Nicaea ...
When the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of 10 days.
However, this article shows that this 10 day shift made Gregorian calendar in sync with Julian between 200 and 300 AD, and the drift between Council of Nicaea (325 AD) and the reform (1582 AD) was in fact 9 days.
It’s simple to calculate that between 325 and 1582, 9 years were leap years in Julian but not in (proleptic) Gregorian: 500, 600, 700, 900, 1000, 1100, 1300, 1400, 1500.
So, why did they choose to shift the date by 10 days? Was it a glaring mistake?