Because they sure had all the rights their ancestors had fought and died for.
They didn't have one right that they had fought for and the Northern states had agreed to. That was the return of runaway slaves. As you no doubt know, there is a clause in the Constitution that addresses this, but Northern states had been flaunting it for years and disobeying the Constitution. The Supreme Court ruled that some of the Northern 'personal liberty' laws that prevented the return of runaway slaves were unconstitutional. Northern states were practicing nullification just like South Carolina had attempted years earlier over tariffs.
Without the runaway slave clause, the Constitution would never have been signed in the first place. The North later backed out of their Constitutional duties. Who was it again who was telling the country how it should be run?
Perhaps the following might answer your question. Again from Jefferson Davis on the floor of the US Senate in 1861:
Is there a Senator on the other side who to-day will agree that we shall have equal enjoyment of the Territories of the United States? Is there one who will deny that we have equally paid in their purchases, and equally bled in their acquisition in war? Then, is this the observance of your compact? Whose fault is it if the Union be dissolved? Do you say there is one of you who controverts either of these positions? Then I ask you, do you give us justice; do we enjoy equality? If we are not equals, this is not the Union to which we were pledged; this is not the Constitution you have sworn to maintain, nor this the Government we are bound to support.