Carson mentions her "contention" towards the end of the piece, because she first wants to lay out the facts for her readers, which implicitly shows how she formed her own opinion, as well as builds credibility (or believability) among her readers.
She likely says what her "contentions" aren't before defining them for two reasons: to disclaim what her readers may have assumed, and to then emphasize what she will say next (what her contentions actually are).
Carson has probably anticipated that by this point in her piece, her negative portrayal of the corporations using pesticides has enforced the idea that she is anti-pesticides in general, which is not the case (thus leading to her disclaimer of what her contentions aren't before explaining what they are).