It is often assumed that the South had better military leadership. Might it be argued that the South enjoyed superior military leadership in the East, at least until 1864, but that the North had consistently better leadership in the West?

Sure. You can argue just about anything as long as you have facts to back up your statements.

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Of course that can be argued. I hear folks argue the US won the Vietnam conflict, because the US got out with honor. I have an exwife that will argue anything, anytime.

So the US Western Campaign:
Halleck, whom Lincoln said was "little more than a first rate clerk"
Sherman, who waged a total "war", meaning he waged war on civilians, mainly. His march through the South was hardly a miliary campaign. We credit Osama bin Laden, and now the Taliban, with the same tactics.
US Grant: The first campaign of Vicksburg was a farce. The second campaign was successful, and yes, Grant outsmarted the opposite side. This was 1863. After that, it was a war of attrition, which is not much dependent on leadership. Wars of attrition means many folks die. It is important to remember that in the Vicksburg battle, Grant had 35,000 troops on the battle line, and the Pemberton had 15,000, cut off from supplies. So did leadership win that battle?
Thomas: Frankly, I like Thomas. He was methodical. He was not a gutless cutthroat like Sherman. His historical demise was mainly due to his uneasy relationship with Grant, who did not serve him well. Thomas was not a glory seeker, and in the post-war period, did not write self-serving memoirs as his contemporaries did.

The question. The first of these "successful" campaigns was in May 1863. Before that, the Union routinely faced rout. Is this consistent better leadership?
Leadership is hard to define, and harder to put on a marking scale. For me, Sherman is a shame, and embarassment. We certainly don't train our Army officers to do what he did, and one officer in Vietnam, was put in prison for it (My Lai massacre). It is too early to judge current history actions on that. Thomas did well, but he had the resources, and he used them wisely and efficently. So I give him a positive mark.
Grant, and Thomas, had the advantage in the 1863 of far greater resources to wage battle, and in the final analysis, this is the deciding factor in a war of attrition.
Your argument suffers for lack of consistent evidence. Good luck. As I started this, anything can be argued.

To evaluate the assumption about the South's superior military leadership, particularly in the East until 1864, and the North's consistently better leadership in the West, we must consider historical events and the key leaders involved. Here's how we can approach this question:

1. Study the performance of Southern military leadership in the East until 1864:
a. Research notable Southern military leaders in the Eastern theater, such as General Robert E. Lee, who was regarded as one of the most skilled Confederates.
b. Evaluate their strategic decisions, tactical achievements, and overall effectiveness.
c. Analyze the performance of the Confederate Army under these leaders, considering factors such as battles won, morale of forces, and how they fared against Northern counterparts.

2. Assess the Northern military leadership in the West:
a. Research Northern military leaders in the Western theater, including Grant, Sherman, and others.
b. Examine their military strategies, decision-making skills, and ability to lead troops effectively.
c. Evaluate the performance of the Union Army under these leaders, considering factors such as victories, territorial gains, and their accomplishments against Confederate forces.

3. Compare the strengths and weaknesses of Southern and Northern leadership:
a. Consider their different approaches to military strategy and tactics.
b. Analyze their ability to adapt to changing circumstances, overcome challenges, and exploit opportunities.
c. Assess the impact of leadership on factors such as troop morale, supply lines, and overall success in battle.

4. Draw conclusions based on historical analysis:
a. Examine historical accounts, primary sources, and expert opinions on the topic.
b. Evaluate the overall performance, achievements, and reputation of Southern and Northern leaders in their respective theaters of operation.
c. Consider any counterarguments or alternate perspectives that challenge the assumption.

By following these steps, you can gather historical evidence, analyze key events and leaders, and form a well-informed argument regarding the assumption about superior military leadership in the South's Eastern theater and the North's Western theater during the American Civil War.