Proper understanding of "dates" related to activities, tasks, etc

I am having real problems understanding how the dates are functioning in the software; consequence is that I cannot close tasks and activities; for example:
I set an action on Monday - Initial due date: 26.June
I want to do it on Wednesday - Planned due date: 28 June; For whatever reason, I cannot take care of this action or I forget to mark it on the software; the status of the Activity is recorded;
Today Friday 30 June, I do all the operation
- allocate the activity to me ( handled:30.06) , then save
- mark the activity done ( done:30.06), save
After that, I want to close this activity, as it is DONE; and I have the error (red stamp with exclamation point - plus result window is marked with a red bar) Indicator: respect of planned due date !
After that, I started messing between accounts - user and Admin, hoping that I can force the closing of this activity but without any luck; I am messing the dates moving them back and forth but the error is still there . . . .
What am I doing wrong ? what is the proper way to proceed and how can I close / cancel some of the tasks, activities, etc without any pain ?

Sorry about that.
It seems to me that in order to be able to CLOSE an activity or a task, one should move the task or activity via entire chain of statuses ...from recorded to qualified, then to accepted / assigned / in progress . . etc . . .up to the CLOSED status.
After that, the only option one can have on a task/activity is to re-open !

What I actually did was to burn some of the steps, for example moving from recorded directly to assigned or directly to closed ! This seems to be not allowed.