Howdy, name neighbor! 
To make a bookmark or automatic embed, the Ghost server has to be able to request data from that url. Sites with anti-bot protection may block this.
You can work around it by generating an embed code (supported by instagram, not sure about medium) and putting it into an html card. Or you can make your own bookmark manually from html, like this: (SOLVED) Edge Theme: editing bookmarks
Or you can use the product card or call to action card to build a manual bookmark.
Be sure to check any of these alternate approaches by sending a preview email. (And check on your phone, too.) Embeds in email wort work if using JavaScript, and HTML doesn’t always translate well.