Why would a delay of N days cause the project's finish date to move by a different number of days?

This is simply the way schedules with non-working days behave.  For example:

• suppose an activity on the critical path that is supposed to finish on a Monday is delayed by one day and finishes on the next day (Tuesday) instead. 
• Also, suppose that before the delay, the project's finish date was scheduled for a Friday.

Assuming a 5-day workweek where Saturday and Sunday are non-working days, the critical delay of one day will delay the project finish date by one working day, which in this case would be Monday.

In this example, a delay of one day to a critical activity delayed the project's finish date by three days because of the calendar.