Learn English – the meaning of the part in bold in the following sentence

Here, the word "very" is used to put additional emphasis on the word it modifies: "first". It's a shorthand for saying

XSLT is a language that, according to the specification — in fact, not just any place in the specification, but the first sentence of it —, is primarily designed for transforming one XML document into another.

Or:

XSLT is a language that is primarily designed for transforming one XML document into another — that's what the specification at http://www.w3.org/TR/xslt20/ says right in its first sentence.

I think it is trying to say that you should not use things that would make your eyes roll when you hear it. For example, if a politician said:"If violent video games are allowed to persist, then everyone who plays them will become serial killers!" Personally I would roll my eyes at this because I know that this is a logical fallacy. One cannot make such as statement without rigorous evidence. We cannot claim that one event (video games) will undeniably lead to another event (serial killers), without substantial evidence.

Essentially, don't use arguments in your paper that, if a politician said it, it would be highly scrutinized.

Hope that helps? Not always absolutely imperative that you understand every sentence in an article, so long as you get the gist of it all. If you don't know a word don't hesitate to look it up as that's the best way to build vocabulary. Well best of luck!