"Arbitrary, capricious, and an abuse of discretion" is all more-or-less boilerplate legalese that was lifted straight out of the Administrative Procedure Act.
It's a reference to a specific level of evidentiary standard that the Act prescribes. Basically, the APA is generally deferential to the agencies deciding how to implement regulations, so challengers have to demonstrate that the implementation in question represents an unreasonable abuse of power.
What it really boils down to, though, is that they're complaining that the FTC didn't make a strong enough case that the burdens this rule imposes on service providers are proportional to the consumer protection benefit.
It's a reference to a specific level of evidentiary standard that the Act prescribes. Basically, the APA is generally deferential to the agencies deciding how to implement regulations, so challengers have to demonstrate that the implementation in question represents an unreasonable abuse of power.
What it really boils down to, though, is that they're complaining that the FTC didn't make a strong enough case that the burdens this rule imposes on service providers are proportional to the consumer protection benefit.