Lysander Spooner was in error.
The people of the US voted for their government. If unwilling to accept the results of elections, the borders of the US were open to anyone who didn’t want that government.
The insurrection was not started to end a US government that they did not want. It started before Lincoln took office, so there was nothing Lincoln did that justified their insurrection.
Rather, it was started to pervert the US government, and force the elected US government (which by election, the people showed that they wanted it) to respond to the desires of a small minority of very wealthy slave owners.
That small minority enslaved the men of the state militias to protect slavery in peacetime, and enslaved them in support of their insurrection.
You characterize everything as having a sharp contrast, when the reality is a lot more blurred.