If you believe the following principles, then your beliefs are incompatible with "democracy":
1) All human beings are equal by nature and moral understanding of our inherent rights, and therefore should be treated equally.
2) Due to this equality, no one has the right to dictate what another human being can or can not do if the action(s) are not substantially dangerous or harmful to anyone, including the human being in question. This is called the non-aggression principle.
3) Force should only be used in self-defense against aggressors committing violent acts such as robbing, assaulting etc..
Most of us in the developed world have been taught that "democracy" gives you the "right to vote", and we should be grateful for that "freedom". It is time to analyze this assertion in-depth to realize the contradictions.
Democracy does not treat nor consider everyone to be equal, as democracy implies a form of government. The body of people labelled government has a perceived right to decide what other people in its jurisdiction can or can't do through legislation. For example:
Governments pass (or try to pass) arbitrary laws decreeing that you can't smoke certain plants or consume a certain amount of soda or junk food "for the good of your own health", but who are they as equal human beings to tell other human beings what they can't put in to their own bodies?
If I came over your house, or your friend's house, and told either of you that I am confiscating any marijuana you have because I don't think it is a smart choice to smoke it, you would most likely and rightfully tell me to get lost: it is none of my business.
However, because this certain group of people has the label of government, they suddenly have the right to tell you the same thing because they think it's unhealthy for you? It is not rational, which is why I called it a perceived right and not an actual, legitimate right.
Freedom, justice and equality can not exist if you have a government, as it makes edicts and enforces them through coercion without exception. It does not matter who or what is in the right or wrong: In the eyes of the law, the law is the only measure of "justice": All laws must be upheld by any means necessary, which certainly includes unjust prison sentences or even the use of deadly force.
Now let's consider our "right to vote": We are allowed to vote for certain politicians, but never is there the option to do away with the flawed system of democracy and government in the first place. Just because the majority of the people or government voted for a specific politician or law, it does not guarantee it was the right and moral choice, nor does it make it the right and moral choice.
This is precisely why no person or group of people should have more power over another person or group of people: It is dangerous, immoral, and irrational. People should not be blindly obeying a group of other people simply because it is written down as "law" and will be backed by threats and the use of force; the actions and decisions people make are no more or less right or wrong if they are legal or not. These actions and decisions will have the same intentions and consequences regardless.
Along with these unfortunate qualities, the concept of government and democracy bestows extra rights to those in government, making anyone else not part of government less of a human being than those in government, which is the most surefire and blatant way to create oppression, inequality and injustice. These extra rights include forcing people to give them money and using it however they see fit, commonly engaging in corruption via this stolen money. Another one of these rights is passing arbitrary laws and enforcing them through any means necessary, as I mentioned previously.
As fellow voluntaryist Larken Rose puts it: Power doesn't just corrupt people. It is corruption.