In Varys' and Illyrio's discussion, Varys talks about how Ned in the position of the hand is stirring up tension too quickly (Bran's fall and looking into Jon Arryn's death) and Illyrio directs Varys to work his magic. So Varys brings this up to the small council knowing Robert would go berserk and banking on Ned to walk away. More @Wikipedia
Hover over any link to get a description of the article. Please note that search keywords are sometimes hidden within the full article and don't appear in the description or title.