I never claimed they were fighting for federalism. But through their own admission in this document, they are clearly opposed to the laws individual states have passed. Their argument is not a state rights argument, it is actually the opposite. They are arguing that other states have taken state rights too far.
The document doesn't spend much time arguing for state rights, instead it begins to indict northern states for the laws they have been passing. Arguments are made about state responsibilities and about the need to reign in other state's rights. If you want to claim the civil war was about state rights, you have to conclude the south was fighting against state rights, not in favor. But that's not the point, the point is that it makes no sense to consider the civil war to be about state rights anyway; it was clearly about slavery, through their own admission.
But neither are you seeing any state rights arguments. We see in every single document of secession, the reason behind it being clearly proclaimed: slavery*.
The bottom line is that an honest reading of any of the secession documents will clearly show what the civil war was all about. Slave-holding states were upset about all of the anti-slavery laws that other states had passed. They saw their institution of slavery being threatened and decided to leave the US in an attempt to try to preserve slavery. That's the bottom line. They all admit it in their documents. An honest reading of any of them will leave you with that understanding.
Even if it didn't, that's just the tip of the iceberg when it comes to the amount of documentation we have on this. If you really wanted to settle it, you don't have to stop at the documents, you could pull up newspaper articles from the time period, you can read the arguments leaders in the South were making around that time, you can read correspondence between various of the people involved, you can read memoirs looking back on the events from some of the people involved. In fact, this thread is about one such memoir that is yet more primary evidence on the mountain of evidence we have showing the civil war was about slavery. That the civil war was about slavery is not the kind of history we are cobbling together from scraps of information; it's the kind we know because we have an overwhelming amount of documented evidence that clearly plays out the whole story for us. The declarations of secession are merely a concise and compelling summary because ultimately, these are the documents the South published in order to explain to you the reasons behind their actions.
*Well, ok...maybe not all of them. Alabama claims they seceded because they didn't like the results of the presidential election. That leaves us having to read between the lines as to why they didn't like those results. But pretty much all of the others make clear that it's about slavery.
Here's a great article providing even more primary sources:
The Confederate Cause in the Words of Its Leaders - The Atlantic
I leave you with the words of the people of Mississippi: