I'm very confused as to the structure of your site, based on Inspect Element. It appears that different sections of your site, such as the sidebars, footers, comments, and other stories sections are strangely mixed together - this may be what is confusing Google as well.
(The following is based on the link you posted that was edited out of your original post)
For instance, if I right click any of the actual text in your story and go to Inspect Element in Chrome, I see the structure as:
html -> body -> div#content -> div#main-body.DIrconflict -> div#main-body-content -> div -> div.wid81.fill.blueline -> div -> div -> div.wid69.fll.lh20.mgr5.mtg5 -> div -> actual text
This seems pretty excessive - are you using a CMS for this site? If it's been customized, I suspect that it wasn't customized particularly well - no offense meant.
As a further point, it appears that the actual text is not in
<p> tags, and is instead just regular text inside of the parent
<div>. Normally, to achieve space between
<p> tags, you could just make a margin on the tag itself - instead, it appears that you place an empty div with a
15px margin between every paragraph - definitely not best practice.
For some further reading about site structure, please check out this page from w3.org - https://www.w3.org/wiki/HTML/Elements/aside - you'll see in the "Point" section, it lists things like quotes, sidebars, advertising, and groups of nav elements. This will help Google figure out your site in order to crawl it - search results will only come from the main content, but it will still learn about new links to crawl from the navigation sections.