Secession and Insurrection have different meanings:Yes it does, the states seceding was considered an insurrection.
Secession is to withdraw from a union.
Insurrection is to openly revolt against a constituted government.
There's nothing about secession that necessitates an open revolt; one can have one without the other, just as easily as one can have one WITH the other.
Given that, the power to suppress insurrection cannot, in an if itself create any prohibition against simple secession.
Secession began 12/24/60. The CSA were formed 2/8/61. The war began 4/12/61.
You can argue, if you want, that an insurrection began 4/12/61, but as secession preceeded the war by a significant period of time, your argument can only stand if you can show that, thru the act of secession, the states did not actually leave the union -- if they HAD left the union, thru secession, then the war was not an insurrectiuon but a war between two states (USA and CSA).
To do THAT you have to show that secession is prohibited by the Constitution, which you -cannot- do by citing the power to suppress insurrection.