Understanding "arrogance" as ad-, to, + rogare, to ask, = arrogance as an "asking" for self that which is irreal or unreal. As Simone Beauvoir said (paraphrasing), "It's not arrogance if you're right." Therefore, arrogance is a "forcing" of a position without corroborating truthness.
Some strategies: understand yourself what are the ontological and epistemological framings of a given "asking" or positing. Truth agreed upon as axiomatic will yet, per Godel's Incompleteness proofs, develop unprovable inferences, i.e., true and false claims that are arrogated without any ability (save a further, second-degree framing) to provide evidence.
Example of arrogance: "I know God is not"--a paraphrase of Sartre; therefore, simple logic re epistemology and the illogical psychologism of claiming to know an absolute negative. In such cases, such illogicality simply indicates fourth-rate philosophy.
Of course, there are many other examples, e.g. in sciences, religions, and arts.
A second strategy, based on the Godelian logic, is to invite epistemological investigation, based on curiosity re the epistemological limits of the arrogating.
A third strategy, based on e.g. Locke's "An Essay Concerning Human Understanding," is to examine the arrogant claims in the light of human psychology (e.g., solipsism as a developmental fixation).
A fourth strategy, based on later Husserl's use of sense and reference, is to develop sense (even spiritualized sensibility) as ontological, and map the sensibility re claim with reference as epistemological; this ~ = bijection of axiomization and system to epistemological bases of "truth." In no case of sufficiently complex axiomization are there to be found unshakeable arrogant (and even humble) truth-claims or falsity-notings. (Cf Hume, and Kant's bifurcated response, which a) assumes a Noumenon and b) a pre-conditioning of phenomenal sensibility per space, time, and causality.)
A fifth strategy, based on one or more of foregoing strategies, is to note such proofs of incompleteness or even of facticity for the arrogating one. In which case(s), if the response of the individual who claims she's a poached egg is to reframe (well, maybe I don't look like a poached egg, but those poached eggs are just one kind of poached egg...I'm another), then one might have to revert to strategies such as Locke's and later Husserl's, or Scharfstein's insights, that the arrogance is driving the philosophy, and not the other way around (i.e., Beauvoir's point).