Image still attached to post even after removing it as featured image

Any image uploaded to a post in the post editor is “attached to” that post. Actually, you can only set an attached image as Featured Image (aka Post Thumbnail — not to be confused with “Thumbnails”), and it’s NOT vice-versa.

If you do not want an image to be attached to a post, you can upload the image directly to the Media Library (via WordPress Dashboard > Media > Add New) and then use the image in your post (from the From URL tab in the media uploader in the post editor).