Sorry however I cannot follow up on these statements

isn’t your post a follow up on those statements?
What other “rights” did certain states claim other than that of taxation?
Wasn’t it a generic claim to order their own affairs and preserve their own institutions, “peculiar” or otherwise?
actually Lincoln a true abolitionist had to promise to not push the issue in exchange for political support. That is the reason he addressed abolition in late 1863 when he believed his election chances were gone. In 1859 the civil war began not late 1863. Additionally in the emancipation proclamation he refused to free any northern slaves!
Because he only had the power to do so in those areas that had rebelled.
Congress or the individual states would have to make laws regarding the legality of slavery in the non rebelling areas.
By 1860 only the Border States and New Jersey (a portion of which lies below the Mason-Dixon line) still had slavery outside of the deep south.
By 1865 when Congress ratified the 13th amendment only Delaware and Kentucky still had it.
Anti slavery language was removed from the declaration of independence
The constitution included language that prevented slaves escaping by crossing state lines and counted slaves as partial persons for apportionment.
The nascent abolition movement of eh 1780s had to roll over on that one or there would have been no nation and no way to eliminate slavery in the future.
The south did not pick and chose, they simply succeeded
Actually they failed

(sorry, it’s that old secede/succeed thing. I couldn’t help myself.)
They picked and chose not to obey the supremacy clause
Had they brought the issue to the Supreme Court in 1860 rather
than 1869 they might have gotten a different a different interpretation. But the law of the land is that secession is not allowed.
I have no problem with the concept of slavery being a deep moral issue. However it simply was not the cause of the civil war.
It was a cause of the war. Wars are complex things, they never have one cause.
Each side probably had much different reasons. The causes for the war are not only why the South fought to secede but also why the North fought to stop them. It takes two to tango.
Slavery may not have mattered a lot to the average southern white that didn’t own slaves
But abolition groups were powerful in the north and it mattered to them. They had spent the previous decades eliminating slavery form the north and were now intent on spreading their views.
The problem is not whether slavery was immoral as practiced. The problem is it was equally immoral when practiced in the Northern US. Many wish to rewrite history simply to claim their ancestry or hometown was void of these actions, the facts simple tell a different story.
The “everybody was doing it” defense doesn’t really hold a whole lot of weight.
So what if there was slavery in the North? Most places in the globe had slavery at some time or another.
Slavery had been dieing out in the north for decades both for practical and moral reasons. The political will to stamp it out nation-wide took decades to develop. When it looked like the political movement had gained sufficient strength the opposition decided to take their ball and go home.