Your question has some kind of paradox! The section name = closed activity, The activity status = closed! It is definitely defined to show closed activities! If you want to not see the closed activities on the navigation bar, simply remove it on the form.
If you want that some types of the activity not to shown, change the conditions of the view. To change it go settings > customizations > customize the system > entity > the desired view > create desired condition. Save and publish the changes.
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