The only reason why there is no "Parent affiliate" field when you are trying to edit some affiliate in the merchant pane, is this:
At Start > Configuration > Affiliate signup > Fields (tab) the 'parentuserid' field is set to "Disabled".
As soon as you set it to any other option and click "Save" at the very bottom of that page and refresh the application (CTRL+F5), the 'Parent affiliate' field will show up in the Details (tab) when editing an affiliate.