“person.” The word “person” (twice in this verse) is iysh (#0376 אִישׁ), which most literally refers to a man, a male in contrast to woman. But it can also be used to refer to men and women, and it makes sense to translate it in a gender-neutral way in this context (see commentary on Prov. 2:12, “the one”).
“disputes.” The usual meaning of “disputes” is to have a controversy in court, although sometimes the word means more of a dispute in general.
“rages or laughs.” The fool is right in his own eyes (Prov. 12:15), and when challenged may either try to bludgeon you with words (Prov. 12:16; 27:3), or, as this verse says, may try to just “laugh you off,” as if what you said was ridiculous. In either case, the fool can make quite a scene (Prov. 27:3), and it is unlikely the case (or the courtroom) will come to a peaceful settlement.