The short form is that the FCC's change can be challenged on procedural grounds, but not on the actual content of the decision.
This article has a couple examples in the section called "Plans for legal action". Specifically:
They can argue that the public record doesn't support the FCC's claim that broadband isn't a telecommunications service, that "throwing away all protections for consumers and innovators for the first time since this issue has been debated is arbitrary and capricious," and that the FCC cannot preempt state net neutrality laws, [consumer advocate Gigi Sohn] said.
The FCC's refusal to do anything about widespread impersonation and fraud in the public comments system, and its refusal to make net neutrality complaints public in a timely fashion, could fuel an argument that the FCC violated the Administrative Procedure Act, she said.
There's other arguments along those lines in the article, but they all boil down to the same type of thing that caused the courts to rule both for and against the FCC in the past: Were all the proper procedures followed to make this rule change?
IANAL, but my impression is that those claims typically fall into a few buckets:
- The FCC doesn't have the authority to do what it did. (This came up in 2010 and 2014)
- The FCC didn't follow all the proper procedures in respect to notification, public comments, and the like.
- The FCC's decision making process used incorrect information, or ignored certain information, or otherwise was misinformed, and thus there was no reason to make a change.
Notably not on the list is "This is a bad change" or anything like that. The rule itself can't be directly challenged, only the process of imposing/changing it.