And since you missed it completely, Lincoln was talking about rebellion, not secession. If he was supporting secession then why would he say "having the power" or "rise up"?
“shake off the existing government” is secession. It is hard to see it through the historical myths the victorious north put forward as history. Perhaps in his heart he knew no state would have the power to exercise their right to secede since the Federal government would unleash all the power of hell to squash the “rebellion” as you see it.