"argument points" is correct and usable in written English.
You can use it when you are referring to supporting evidence for an argument that you are making in an essay or discussion. For example: "I have several strong argument points to support my position on this issue."
The economic argument points to the league's paid attendance, for instance, which is very high.
Simon's argument points to a tenet of Petraeus's command philosophy, one that might be called constructive opportunism.
But that argument points to the extra challenge their side faces: The opposition is divided on the strike.
The procommunity argument points to the many ways people get together online to chat, gossip and give each other support.
(Time's Christopher Matthews, in making this argument, points out that Paul Krugman also used to make it in his pre-firebrand days).
The cricketing argument points to retaining Batty if the ball is going to spin excessively from the start, but to stick with Rashid if the pitch is flatter.
The exchange, obtained by the Oxford Mail, shows Hudspeth taking issue with Cameron's argument point by point.
USAID's head, Rajiv Shah, is optimistic that the reformers will win this argument, pointing to a fiscal environment in which every dollar must be made to count.
Critics dismiss that argument, pointing to the Harper government's promotion of the Alberta tar sands and its opposition to the Kyoto protocol agreements on climate change.
But the commission rejected that argument, pointing out that, for example, surgical sterilization is covered by the plan, as is Viagra, even without a finding of impotence.
Although Smith dismisses this argument, pointing out that Cerner provides "the primary mission critical IT system for the entire hospital" versus DeepMind building just an app.
