There are many good arguments and plenty of historical evidence of why any suggestion of a parliamentary road to abolishing the State, even in an advanced liberal democracy, is extremely unlikely. There is the argument that parliament is innately a bourgeois parliament that excludes substantive reform which is won by extra-parliamentary means. Then there's the argument that parliament will corrupt and weaken any who attempt reform. Finally, there are arguments that any threats to it will result in violence by the ruling class to protect their privileges. These arguments have a degree of legitimacy, however, they are not the point of this discussion. Rather, it is the identification of the special privileges embodied in law that create economic classes and thus a State. In doing so one can, at least in a pro-forma sense, map out what changes would be required to abolish the State through such a means.
In the first instance, it is necessary to differentiate between "the State" and "government". Many anarchists, like most people, have conflated and confused the two, but there is much to be gained by making a distinction. Bookchin [1] notes that whilst all states have governments, not all governments are states. "A government is a set of organized and responsible institutions that are minimally an active system of social and economic administration. They handle the problems of living in an orderly fashion. A government may be a dictatorship; it may be a monarchy or a republican state, but it may also be a libertarian formation of some kind". Proudhon, the first person who identified politically as an anarchist, argued: "Anarchy is... a form of government or constitution in which public and private consciousness, formed through the development of science and law, is alone sufficient to maintain order and guarantee all liberties."[2] Etymologically the two differ; governance means "to steer" (from the ancient Hellenic "kybernan"), whereas anarchy, rather than the early modern English usage of "disorder", means to have no archon, or ruler, i.e., "no ruler", not "no rules". In contrast the state is from the Latin, "stare", "to stand", where we also have such terms as "estate".