What kind of federal interference are you talking about, and what Constitutional violations were they protesting?
The opening portion of the declaration outlines the historical background of South Carolina and offers a legal justification for its secession. It asserts that the right of states to secede is implicit in the Constitution and this right was explicitly reaffirmed by South Carolina in 1852. The declaration states that the agreement between South Carolina and the United States is subject to the law of compact, which creates obligations on both parties and which revokes the agreement if either party fails to uphold its obligations.
The next section asserts that the government of the United States and of states within that government had failed to uphold their obligations to South Carolina. The specific issue stated was the refusal of some states to enforce the Fugitive Slave Act and clauses in the US Constitution protecting slavery and the federal government's perceived role in attempting to abolish slavery.
The next section states that while these problems have existed for twenty-five years, the situation had recently become unacceptable due to the election of a President (this was Abraham Lincoln although he is not mentioned by name) who was planning to outlaw slavery.
The final section concludes with a statement that South Carolina had therefore seceded from the United States.
Of course you are free to disagree, but SC position was that the Constitution was a agreement between the federal government and state governments. SC believed that the federal government was not holding up their end of the agreement, so SC wanted out of the agreement. Under the 10th Amendment, the unenumerated right of secession is obviously a right reserved to the states, so SC was fully justified in taking this step.