Really, when you think about it, the entire Declaration of Independence is a Declaration of Dissatisfaction. The whole reason for the document's existence is anger and disapproval of the actions of the government. Jefferson repeatedly argues that the British government has done things they shouldn't, and that is why the colonies must be free, going into pretty solid detail about all the shenanigans that have been pulled by the King and Parliament.
Dissatisfaction may seem at first like a tame word for what's going on, and there are certainly more dramatic themes in there. As mild as may seem, though, dissatisfaction underlies almost everything written in the Declaration.
Jefferson's complaints about the British government distract from the primary purpose of the Declaration of Independence, and make the document really about something else entirely.
Jefferson had to elaborate heavily about the colonies' dissatisfaction with Britain in order to be taken seriously and not seen as ungrateful or hasty in their decision.
Jefferson consistently uses the juxtaposition of freedom and tyranny throughout the Declaration of Independence. King George and Parliament represent tyranny, while the people of America represent freedom. Jefferson compares the two, sometimes directly, sometimes by implication, as a way of illustrating the colonies' justification for their declaration.
Freedom also comes into play in a more literal sense, since the document serves to give the colonies' legal freedom from their former rulers. More significantly, Jefferson's device of comparing the two opposing ideas emphasizes the differences between the colonies and Britain, as if to say that the colonies are independent regardless of their official status.
Although Jefferson provides many examples of the tyranny of the British, he doesn't fully explain how the United States will provide an alternative (freer) method of government.
The primary reason Jefferson leans on the freedom vs. tyranny theme is more rhetorical than logical. He is using the juxtaposition as a device to convince people to support an independent America.
Principles are fundamental ideas about how people should behave, or how the world should operate (except in science, but that's not really what we're discussing here). In the Declaration of Independence, Jefferson discusses the reasons why the British government has acted wrongly and therefore lost the right to govern the colonies.
By arguing that the colonists have certain rights as human beings, which should be protected by the government, Jefferson and the Continental Congress are proclaiming that the King and Parliament's actions have not been morally right. The Founding Fathers are adhering to certain principles to determine their vision of how government should be, and to prove how the British government has failed.
The principle of good, benevolent government is big for Jefferson, and is really the main idea of the Declaration of Independence.
Jefferson provides more evidence for the lack of principles on the British side then for the presence of principles on the American side.
Jefferson and the Committee of Five made sure the Declaration of Independence didn't just, you know, declare independence, but gave a multitude of legitimate reasons for doing so. Jefferson also threw in some lines showing that the colonists' knew what they wanted (or didn't want) from a government, proving that these uppity rebels understood what a government should be, and therefore were capable of governing themselves.
The Declaration was the first official document of the United States, and it had to prove that the United States had a legitimate cause and right to exist as an independent nation, and should be considered an equal.
Jefferson needed to prove that the colonies were a legitimate nation, because otherwise the Declaration of Independence would merely be seen as part of their angsty teenage rebellion against the Crown.
Jefferson provides lots and lots of evidence to support the legitimacy of the colonists' argument. His effort implies that either the colonies felt that their complaints had been ignored, or that they weren't confident that the British government would take their claim seriously.
The most obvious presentation of the idea of equality in the Declaration of Independence is the part we all know and love (hint: the word "equal" is in the sentence). That sentence has echoed throughout American history.
We now know that the 18th century version of "equality" was super-incomplete, but even bringing up the idea that men were born equal was relatively new, especially in a public document. Jefferson also includes moments that show the colonists' desire to be considered equals of their fellow citizens in Britain, and how that desire has been ignored in recent decades.
Jefferson had to say all men were created equal, not just the colonists and the British, because a grand sweeping philosophical statement is way harder to argue with.
Along with that famous line about equality, the theme is in the background throughout the whole Declaration, because Jefferson is accusing the British government of treating the colonists as inferior subjects.