The history of slavery in America is very long and complicated, and covers aspects that go beyond objective facts and enter the realm of psychology and sociology. Based on this alone, dates, facts and figures do not suffice to explain the human psychology underlying radical changes in the history of slavery, however, it is indeed a good start.
What had changed in 1860 was that the Republicans had won power, and this was ultimately the biggest factor in the demise of slavery at that time. The Republican covenant during their era was to diminish the existence of slavery.
Aversion to this policy and constriction of Slavery eventually lead to a civil war. This ultimately saw the collapse of the whole system of slavery in the USA.
President Lincoln's main ambition for the civil war was to rescue the union, above abolition of slavery. He is quote to have said,
“If I could save the Union without freeing any slave, I would do it,” the president stated, “and if I could save it by freeing all the slaves, I would do it.”
However, the pressure to abdicate slavery was so strong that this ended up being the ultimate goal of the war. In 1863, Lincoln issued a proclamation to end officially slavery. By 1865, this was fully legalised and slavery had ended "legally" in the USA for good.