Is the Task promised or completed?
If deleting your tasks isn't working, that may be because the Tasks you're trying to get rid of are either promised or completed.
When a Task is promised, the start and finish dates assigned to get locked down. Any changes made to the dates of Tasks in this state get recorded as statuses.
From here the only users on a project that can delete promised or completed Tasks are Admins. This is done as a means to ensure that delays are being accurately captured at all times.
Do you own the Task?
It's also possible that you do not have permission to delete the Task. Only the Task Owner or Project Admin can delete a Task. Assignees or Delegates cannot delete an Owner's Task.