The phrase "argument for him to" is correct and usable in written English.
It can be used when discussing a reason or rationale that supports a particular action or decision for someone.
Example: "There is a strong argument for him to reconsider his decision about moving to another city."
Alternatives: "case for him to" or "justification for him to".
"This was a good argument for him to receive the job," Mr. Pavlov said.
It is a delicate argument for him to make because Aventis is the product of a huge merger that executives at the time said would yield great synergies.
Those questioning whether Ronaldo even deserves to be on the podium, however, should recognise the strong case for his presence and why there's even an argument for him to win.
McCain doesn't have the nomination yet but if he gets it there's a compelling argument for him to pick Colin Powell as his veep.
But at the end of our chat, I couldn't remember why, or think of any more arguments for him to answer.
Read in today's context, every corporate value that Zuckerberg reels off in the letter are arguments for him to emerge from hiding.
"I think if Martin had received real enthusiasm from Twickenham to carry on even for the next six months, there would have been a strong argument for him [to do so].
If an economist is falling behind in an argument, a good way for him to regain the initiative is to play the transparency card.
The only way for Obama to win this argument about change was for him to raise the character issue, which he had tiptoed around until that point in the campaign.
The fact is that for any public figure to go with the Congress-did-it argument at this stage is for him to reveal both that he is grossly ignorant about the central policy issue of the day and that he gets his "analysis" from right-wing flacks.
Asked if he bought those arguments, Thornberry said it wasn't for him to "buy or sell the argument".
