The Second Vatican Council teaches nothing of the sort. The church’s hierarchy was established by Jesus Himself and can never be changed into a democracy, because a democracy by definition has no hierarchy. The Church’s structure was patterned after the structure of heaven, which is an absolute monarchy with God on the throne. He is the ruler, and we are his subjects. He appointed a prime minister, Peter, to rule in his absence, investing him with much of his own authority as king and shepherd (Matthew 16:18-19, and John 21:15-19). He gave Peter chief assistants, the other apostles. This pattern of government continues today through apostolic succession in the pope and the bishops in union with him.
So why do we have parish councils? Not because the Church has been changed from a monarchy into a democracy. Terms like these properly should be reserved for political institutions only. Pastoral councils have several practical purposes: to relieve parish priests of administrative burdens which can be accomplished as well, often better, by parishioners; to give the pastor feedback from the pews; and to develop a pastoral plan for the parish. In all these the council is a consultative, not legislative, body. It makes recommendations to the pastor, but doesn't usurp his authority or duties. The pastor cannot abdicate his authority (which comes from the bishop) to a parish council, but he may delegate as much of it as necessary. Of course, he can’t delegate his purely sacramental functions, for which ordination is required.