hyunah and yang_dong,
You both seem to be having a similar problem so I'll clarify:
''why might the author have chosen this wording/phraseology in particular? How does this choice contribute to our thoughts/feelings towards the issue?"
For example, an author might write: "The ongoing war between the government and special interest groups regarding the issue of __ has divided the local community." (<-- very bland sentence btw. you wouldn't use this in an actual essay)
Why has the author chosen 'war' in particular. There are many other words he could have chosen: dispute, conflict, disagreement, clash, quibble. Yet he chose war, with its connotations of bloody battle and global consequences. In this case his word choice is hyperbolic, since there is no official war between these two groups; the author merely attempts to exaggerate the degree of fervour surrounding this issue.
He could have said 'quibble,' connoting a petty and insignificant disagreement, which would have inferred the issue is not worth discussing. Or he could have written 'an arduous, tiresome crusade on behalf of these activists' which sets up the group as brave and resolute.
Not every word will be this obvious, and not every word is important. But often you can work out where to take your argument based on how the author is positioning the readers through language at word-level.
You're on the right track with the connotations, but the problem doesn't seem to be phrasing, just the idea behind it. How does the author want us to think/feel? And how do you know this? That's pretty much all you have to answer.
Beyond that, I don't know much about the issue/articles to comment on either of your pieces but
hyunah: the author isn't focusing on the happy ending, he's using double negatives, sort of. 'Back then, no one was suffering': implying that they are now. He draws these parallels between what was and what is, in order to draw attention to the backward progress we have made. etc.
yang-dong: if you've written the same synonyms too often, then you've probably made the same point too many times too. Group persuasive devices, don't go through articles chronologically because you'll end up with a mess of an essay. In this instance, yes, the Liberals are better equipped to deal with the issue but that's not all this sentence does. Look at the implication, if Liberals are adults what does that make Labour? (A: childish, petulant, naive, puerile etc.)
Hope that helps.