some sites protect their images against users downloading them.
Perhaps this is what is happening to you.
Post a link to a site where it is happening.
On my new iMac I used to be able to save photos from the web by right clicking "save image as" and directing it to a folder. All of a sudden now when I click "save" I get the message "The document could not be exported. You do not have permission. To view or change permission, select the item in the Finder and choose File>Get Info. I can't get this to save the photo. How do I get back to the old way?