What is the reasoning behind Lincolns referring to the South as the rebellion?

That on the first day of January in the year of our Lord, one thousand eight hundred and sixty-three, all persons held as slaves within any State, or designated part of a State, the people whereof shall then be in rebellion against the United States shall be then, thenceforward, and forever free; and the executive government of the United States, including the military and naval authority thereof, will recognize and maintain the freedom of such persons, and will do no act or acts to repress such persons, or any of them, in any efforts they may make for their actual freedom.
That the executive will, on the first day of January aforesaid, by proclamation, designate the States, and part of States, if any, in which the people thereof respectively, shall then be in rebellion against the United States; and the fact that any State, or the people thereof shall, on that day be, in good faith represented in the Congress of the United States, by members chosen thereto, at elections wherein a majority of the qualified voters of such State shall have participated, shall, in the absence of strong countervailing testimony, be deemed conclusive evidence that such State and the people thereof, are not then in rebellion against the United States.
That attention is hereby called to an Act of Congress entitled “An Act to make an additional Article of War” approved March 13, 1862, and which act is in the words and figure following:
‘‘Be it enacted by the Senate and House of Representatives of the United States of America in Congress assembled, That hereafter the following shall be promulgated as an additional article of war for the government of the army of the United States, and shall be obeyed and observed as such:
Article —. All officers or persons in the military or naval service of the United States are prohibited from employing any of the forces under their respective commands for the purpose of returning fugitives from service or labor, who may have escaped from any persons to whom such service or labor is claimed to be due, and any officer who shall be found guilty by a court-martial of violating this article shall be dismissed from the service.
SEC. 2. And be it further enacted, That this act shall take effect from and after its passage.”
What is the reasoning behind Lincolns referring to the South as “the rebellion”?
Why does he continually use this term?
Be sure to use evidence from the text to support your answer.