Why can’t I see the link preview in my Twitter post?
This happens when the link is not validated by Twitter - Twitter Cards, for that tweet, is not properly defined.
To check whether the URL is validated by Twitter, visit this page. If your link generates a preview here, it will definitely generate a preview when it's published from your Twitter account.
However, if the validator doesn't crawl the meta-data and shows an error, then the link is not validated by Twitter. Consequently, the link will be published as a plain text. We suggest you check all your links using the Twitter Card Validator.