“You claim Lincoln is advocating a right to secession when in fact he’s talking about a right to rebellion.”
That’s a distinction without a difference, because they are the same right! The right to self-governance, aka the right to self-determination. The only difference is in the method being employed to exercise the right.
Secession implies a peaceful, legal, orderly process while rebellion is the exact opposite. Lincoln is obviously talking about rebellion since he adds the qualifier "...and having the power...". Why do you need power if your parting is by mutual consent?