What does “your analytical argument” mean?

Suppose the sources establish:

Zietlow

The Thirteenth Amendment helped transform the legal order from unfree to free labor.

Kolchin

Formerly enslaved people sought autonomy and economic security but faced unequal power and land poverty.

You then reason:

If legal freedom existed but access to land and economic resources remained highly unequal, then legal freedom did not automatically produce economic equality.

That final proposition is your analytical inference.

It is not necessarily a direct quotation from either historian.

Example

Evidence:

A has legal freedom.

Evidence:

B has unequal access to land.

Your reasoning:

Therefore, A did not automatically eliminate B.

That is your synthesis of the evidence.

This is normal historical scholarship.

Why is the distinction important?

Because you should write:

Kolchin (2024) argues X.

when Kolchin actually argues X.

But if you combine Kolchin's evidence with Zietlow's evidence and draw your own conclusion, you should write:

Taken together, these developments suggest that...

or simply state your analytical conclusion and support it with the relevant citations.

So:

cite the historian for the historian's proposition; make clear when you are drawing your own inference from multiple sources.

That is methodological honesty.