Eiruvin 13b records a dispute between Beit Hillel and Beit Shammai that went on for three years, after which a bat kol (voice from heaven) intervened. The point of bringing this story here in the g'mara seems to be to expound on why the bat kol ruled the way it did, not to talk about the dispute. and it doesn't actually say what the dispute was. (I don't think they were arguing about being half-in a sukkah; that seems to be evidence for the conclusion, not the source of the problem.)
What were they arguing about?
Note: farther down that page we get the 2.5-year-long dispute about whether man should have been created. This is not that.