"Read the book I just wrote which proves that what I think is correct, because it's in that book I just wrote. "
Of course he/she/it left out this important piece of evidence. The Union was going to keep slavery.
So how does he/she/it figure that the Union was fighting a war to end slavery?
You are aware that when Lincoln sent that letter to Greeley he had already presented the first draft of the Emancipation Proclamation to his cabinet? And that the last line of that letter he clearly stated that his personal preference was an end to slavery?
“So how does he/she/it figure that the Union was fighting a war to end slavery?”
The United States Government was obligated by the Constitution to suppress the unlawful Rebellion:
Constitution
Article. IV.
Section. 3.
New States may be admitted by the Congress into this Union; but no new State shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or Parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress.
The Congress shall have Power to dispose of and make all needful Rules and Regulations respecting the Territory or other Property belonging to the United States; and nothing in this Constitution shall be so construed as to Prejudice any Claims of the United States, or of any particular State.
Section. 4.
The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened), against domestic Violence.