I have created a subsite, but for some reason (my lack of knowledge) I cannot open it in SharePoint designer. This was one of six subsites I created, and only this one site has issues. the message I get is: "You do not have permission to open this Web site in SharePoint Designer." Dialog box title is "Microsoft SharePoint Designer".

You should be part of Site collection administrators group or Designers group or  Owners group to open site in SharePoint Designer. Make sure you are part of one of these groups.