The phrase "an argument why" is a correct and usable phrase in written English.
You can use it when you want to introduce a reason why something is true or should be done. For example: "I would like to present an argument why it is important to recycle."
I could make an argument why he deserved to share in the Nobel Prize".
"The first significant discovery we shall make as we racket along our female road to freedom is that men are not free, and they will seek to make this an argument why nobody should be free".
Is that an argument why they shouldn't be running health care?
In this paper, we start with an argument why it is problematic to define the role of network companies on the basis of the economic, legal, technological, political and policy points of view.
Naturally, we need an argument why this faculty cannot be identified as belonging to the self, and the usual Nyāya claim is that the self is the agent of cognising, while the mind is an instrument for cognising, just as we must distinguish between the axe-man, who is the agent chopping the tree, and the axe, which is the instrument for chopping.
Logic might thus tell us at least this much, though: whenever I have some reason to believe A and if A then B, then I have a prima facie reason to believe B. See (Harman 1986) for the view that logic has no distinctive normative role, and (Field 2009) for a nice critical discussion of Harman's view and an argument why logic should be tied to norms of rationality.
Each time a study doesn't replicate, "they make a specific argument why the studies are different," Young says.
Anyone still needing a good argument why New York should choose its judges through a merit-based system need only look to the latest shameful episode in Brooklyn.
It never did produce a convincing argument why, but, all the same, so many athletes were tainted.
