I have not been deep in the weeds of the arguments about Section 3 of the Fourteenth Amendment, unlike my constitutional law casebook coauthors: Mike Paulsen, Michael McConnell, and Will Baude. But it is surprising to me that the former President of the United States seems to be putting most of his legal eggs in one basket—the argument that the President is not an "officer of the United States." This is the lead argument in the brief available here. And for reasons I cannot understand—as a matter of legal principle—this argument is now being advanced by various conservative legal luminaries.
Three observations:
1. The textual arguments advanced in the brief are weak, but the fundamental problem is a lack of sophistication about the interplay between semantics and context. Here is an example from pages 23-24: "every time this phrase appears in the Appointments Clause, the Commissions Clause, and the Impeachment Clause it excludes the President and refers only to appointed and commissioned officers rather than elected officials."