to make war on someone: to attack an enemy in open, sustained conflict, and so to be locked in hostility with them.
This verb names the act of going to war rather than the conflict that results. The related noun "war" (πόλεμος) names the fighting itself; this word names attacking, which is why it almost always has a target attached to it. It is not the word for soldiering as a career (στρατεύω), and it is stronger than simply falling out with someone.
Six of its seven New Testament appearances are in Revelation, and there the fighting runs in every direction. The beast and the kings of the earth make war on the Lamb and on God's people, Michael and his angels make war on the dragon, and Christ himself makes war twice: once on a faction inside the church at Pergamum, and once as the rider on the white horse who "judges and makes war" in righteousness. In both of those last cases his weapon is the sword of his mouth, a spoken verdict rather than a blade, so the war language stays serious without turning into a picture of ordinary battle.
James alone turns the word on a congregation. "You fight and wage war" sets it beside the everyday word for quarreling (μάχομαι), and the jump from one to the other is the point: what the readers experience as ordinary friction over what they want is, in James's telling, open hostilities.
Nuances
Whether James 4:2 describes actual violence among its readers or applies war language to bitter quarreling within the community.
- majorityThe war vocabulary is rhetorical escalation: the conflict in view is envy, rivalry, and quarreling inside the community, not literal armed fighting.; BDAG, s.v. πολεμέω 2; Peter H. Davids, The Epistle of James, New International Greek Testament Commentary
- minorityThe language reflects genuine social violence in Palestine before the Jewish war, so more than metaphor may be in view.; Ralph P. Martin, James, Word Biblical Commentary 48