The phrase "argument section" refers to a part of a discussion or essay where you provide reasons or evidence to support your opinion or point of view. Full definition
For more info on these please read the full new legal arguments section below so you understand exactly what you will be taking to court. (moneysavingexpert.com)
The teacher should then show the students a copy of the Petitioner and Respondent's brief (with the argument section omitted.) (edutopia.org)
Once you have done that twice, you have the three basic sections needed for your appellate brief: the cover page, the section containing the various preliminary information, and the main fact and argument section. (lawyerist.com)