Why is it methodologically stronger not to pretend that cited scholar made your exact argument?

Because there is a distinction between:

what a scholar actually argues

and:

what you infer by applying the scholar's framework to your own historical case.

Suppose Smith says:

Legal citizenship and lived citizenship are distinguishable.

You then reason:

Therefore, this distinction helps explain why formerly enslaved people could possess legal freedom without immediately being treated as social equals.

That second sentence is your application.

It is perfectly legitimate.

But if you write:

“Smith argues that emancipation failed to produce social equality among formerly enslaved people,”

you may be attributing to Smith a specific historical argument he did not actually make in that passage.

That is why the academically cleaner structure is:

Smith (2022) distinguishes legal citizenship from lived citizenship...

Then:

This distinction is useful for understanding the post-emancipation South, where...

The first is Smith's argument.

The second is your analytical application.

That distinction is very important in scholarly writing because it prevents citation inflation—using a scholar's authority to support a proposition that the scholar did not actually make.