The Julian calendar is slow by 0.75 days per century. Like fixing the time of a slow clock by moving its hands forward, in 1582 it was decided to fix the date of the slow calendar by moving it ten days forward.
Why ten days? Why not nine or eleven?
If you ask a search engine this question, you’ll find lots of texts repeating the information that they wanted to restore the calendar as it was in 325 A.D., the date of the First Council of Nicaea.
But the number of additional leap days in the Julian Calendar from 325 to 1582 is one for each of the years 500, 600, 700; 900, 1000, 1100; 1300, 1400 and 1500. A total of nine days. Or, another way to calculate it, (1582 - 325) / 100 * 0.75 = 9.4 days.
Why ten days?
To get the answer, we need to unearth the Pope’s 1582 decision. There, it says that they have arranged “to restore the vernal equinox to its original place from which it has already receded by about ten days since the Council of Nicaea”. A little bit further below it becomes more specific, decreeing that the vernal equinox is to be restored to the place where it “was placed by the fathers of the Council of Nicaea at the twelfth day before the Kalends of April” (this is 21 March).
Conclusion: always look up the original reference.
Here’s a similar question: Was the 1582 decision right in that the Council of Nicaea had placed the equinox on 21 March? Again, we’d need to consult the original reference, but it seems that the relevant part of the Council proceedings has been lost.