Here is the salient portion. I'm taking the liberty of bolding a line or two:
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.--That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed, --That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness. Prudence, indeed, will dictate that Governments long established should not be changed for light and transient causes; and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed. But when a long train of abuses and usurpations, pursuing invariably the same Object evinces a design to reduce them under absolute Despotism, it is their right, it is their duty, to throw off such Government, and to provide new Guards for their future security.--Such has been the patient sufferance of these Colonies; and such is now the necessity which constrains them to alter their former Systems of Government. The history of the present King of Great Britain is a history of repeated injuries and usurpations, all having in direct object the establishment of an absolute Tyranny over these States. To prove this, let Facts be submitted to a candid world.
It's an inspirational document and well worth revisiting from time to time.
The two bolded sections complement one another and the whole paragraph is followed by a recitation of specific, enumerated claims providing evidence to their complaint of tyranny. I would also point you to the paragraph following the complaints where they mke note of their efforts at remediation:
In every stage of these Oppressions We have Petitioned for Redress in the most humble terms: Our repeated Petitions have been answered only by repeated injury. A Prince whose character is thus marked by every act which may define a Tyrant, is unfit to be the ruler of a free people.
So the DOI does not acknowledge any right to unilaterally break the bond of the republic for frivolous reasons - such as a government "not to their liking". It does strongly advise against abandoning all the hard work that was done to create our republic for "light and transient causes".
According to Diogenes, it's okay to do it if someone hurts your feelings by saying that slavery might be a bad thing.
Before I sent you the last message, I told myself "He's gonna come back with "light and transient causes...". "It is the only arguing point he has in the document."
So you think the Southern states concerns were "light and transient"? Would you care to elaborate?