The verb means to reproach or scold in a loud and abusive manner. Calvin, on 1Co 4:12, “being reviled we bless,” remarks: “Λοιδορία is a harsher railing, which not only rebukes a man, but also sharply bites him, and stamps him with open contumely. Hence λοιδορεῖν is to wound a man as with an accursed sting.”
His disciple (μαθητὴς ἐκείνου)
Literally, that man's disciple. The pronoun has a contemptuous force which is not given by his.