Democratic right

A political commentator from Novara Media on tv recently claimed on behalf of people their 'democratic rights'. But what are they and was she right? As with most of these 'rights' we can trace their origin in the United States Declaration of Independence which includes these words:
"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."
I suppose if you are US citizen it pays therefore to be a believer in God, thereby sustaining these 'unalienable rights'. But what relevance are they in reality?
Firstly, it is palpably untrue that all men are created equal. They are all different, not only physically, and one of the major differences lies in the fact that there are born leaders and born followers. It is mentioned because of the USA's shame about the history of slave labour and abuse of black workers, particularly in the South. The sentiment is re-inforced by the second term, 'Liberty' that allows the prospect of men and women being free to follow their own inclinations; to have free will under the law. It suggests to me that these rights are more to do with administration shame than it does with actual reality. Nobody has a right to anything except the chance to continue in existence, to have the opportunity to live their natural life whether it be long or short. ie one has a right not to be murdered. There are no other rights. None. There can be no rights to be happy or to pursue happiness in the same way that no one can have the right to be free from illness. It's an ambition, not a right. It's the same about democracy; it is not a right to live under democratic rule and therefore a it is a fallacy that there can be democratic rights.