More than likely this is because you are adding a News Item that is only published on a secure page like a Community Group Page.

Because Community Group Pages are only accessible when logged in, it will prompt Users to login in order to see the Content.

You can create a new News Category, and share the News Story to the new News Category so it makes the item now "Public"
  1. To create a new News Category, navigate to:
  2. Core > Content > News or School Website > Content Types > News
  3. Click + Add New
  4. Title the News Category
  5. Click Save

To share this to the new Category created:
  1. Edit into the News Category that existed prior to creating the new News Category
  2. Click Add More
  3. Expand Page Content, and mark the new News Category you just created above