Final answer:
The detail illustrating Lincoln's statesmanship as a contextual skill is his approach to dealing with the challenges of emancipation and reconstruction, while prioritizing the preservation of the Union.
Step-by-step explanation:
The detail that best supports the writer's idea that "statesmanship is not an abstract skill, but a contextual one" is found in the passage describing how Abraham Lincoln, in the context of civil war, had to adapt his policy positions and actions to the shifting tides. During his presidency, Lincoln was faced with the interrelated questions of emancipation and reconstruction, and he believed that the union's preservation depended on careful strategic decisions such as the choice of Cabinet members and the tone of his inaugural address. By taking steps like supporting gradual compensated emancipation and seeking to balance political and military goals, Lincoln demonstrated statesmanship that was deeply rooted in the complex context of his time.