What is a democracy? - "a government in which the supreme power is vested in the people and exercised by them directly or indirectly through a system of representation usually involving periodically held free elections". So we can say that in the democracy people by the votes decides what directions has to be taken and it is done by elected representatives. There are many pros and cons to it but this is not what I want to talk about.
The Church is hierarchical. What a hierarchy means? - originally - "the ranks of different types of angels in the celestial order". Of course this is extended to God as the first and then everything goes down until it reaches people. So it means that the head of the Church is not a pope but God himself. Why it is important to understand that? Because there is no place for a democracy within the Church. There are few reasons for it and I will talk about few of them.
Democracy doesn't have an authority. The person elected as a representative of a group of people can change the meaning of intent of electorate without any responsibility. They claim to have one but it is not an authority but a power. In the Church the authority belongs to God only. Each bishop, priest receives the faculties to preach the truth but it has to represent the truth coming from God. The weakness of the Modern Church is not in the lack of the authority, but in the fear of people, instead of the fear of God.
Democracy sooner or later doesn't represent people anymore. Because of the lack of responsibility among the majority of the voters, the elected person receives a power that allows manipulate the truth and the people. As consequence people do not follow the facts but their emotional preferences. In the Church the truth is independent from any personal, emotional position of the person. God, who is an absolute truth doesn't change His truth according to the desires of creation. The weakness of the Modern Church is that even the Word of God is translated very soft way, loosing the same time the depth of the God's message.
Democracy turns very often into the dictatorship. The same people elected for decades create the law that will protect their position and the same time will give a profit to their own people (lobbies). Historically we can see it in the ancient Greek and Rome. Both democracies died by a very terrible death. The weakness of the Modern Church is that we try to apply democratic rules into the structures of the life of the Church without understanding the the truth cannot be change by the vote or acclamation. Non of the bishops, priests represent the personal truth and rule it over the people. The truth comes to people through the work of the "unprofitable servant".
So to make it clear: there isn't democracy in the Church. A creation cannot rule a creator. God is Love - we as people cannot make a new definition of love, because it would be a lack of love. God is truth, so we cannot create a new truth because it will be a lie. God is life, so we cannot create a new meaning of life because it will lead us to the death.
By the way I am amazed how many Americans do not know what political system we have in USA. We are a democratic republic and we have a federal government. Please, tell this to your children, families and friends.