When you inactivate a task in Project 2013 that has a predecessor and successor, the successor task is now linked to the inactive task's predecessor. This is new behavior in Project 2013 from Project 2010.
Consider the following scenario:
You have three 5 day tasks linked together with a finish to start relationship. The first task's start date is June 1st, second task is June 7th and the third is June 21st. You inactivate the second task, the start date for the thrid task is now June 14th.
In Project 2010, when you inactivate a task that has both a predecessor and a successor, the successor task's start date would revert to the start date of the parent task. This could mean that the successor task would begin at the project start date, causing the project Finish date to recalculate.
Using the same example as above, when you inactivate the second task in Project 2010, the last task's start date is now June 1st.
Proj2013, inactive tasks,