The phrase "arguable case" means that there are reasons for and against a certain viewpoint or argument, and it is possible to debate or discuss it. Full definition
Orexim's s. 423 and declaration claims did not show a good arguable case of falling within a jurisdictional gateway. (st-philipsstone.com)
Berger's is in many ways a minimalist Christian proposition, but there is an at least arguable case to be made that it is all that we can with integrity sustain. (firstthings.com)
The correct test where the claim has a real prospect of success is in three stages: to consider (i) whether the children had a seriously arguable case that they would succeed at trial in obtaining a proprietary interest in the property; and if so (ii) whether either or both parties would be adequately compensated by a damages award; and if not (iii) where the balance of convenience between the parties lies. (newlawjournal.co.uk)