arrogant: the person who inwardly sets himself above other people, and above God, and so looks down on them
This word names a very particular kind of pride. It is not the loud bragging of the show-off, nor the bullying cruelty of the person who tramples others for sport. It is the quiet, inward attitude of someone who has decided he stands higher than everyone around him, and who therefore holds them in contempt. The picture built into the word is of a person who makes himself conspicuous, who towers over the rest, at least in his own estimation. Its home is the heart, before it ever shows up in words or actions.
Greek writers before the New Testament used it mostly this way, for the haughty and overbearing, though once in a while they could stretch it to mean splendid or magnificent. The Bible drops that positive shade completely: here the word is always an accusation. When the Old Testament was translated into Greek, this one word was chosen to carry a whole shelf of Hebrew words for pride, and in the process it took on a sharp edge. The arrogant person became, above all, the one who lifts himself up against God.
That is why the same short saying keeps returning in the New Testament, quoted almost as a settled formula: God lines up against the proud like an army facing an enemy, but gives grace to the lowly. Mary sings that God scatters the proud in the secret thoughts of their hearts. Paul lists the proud among people who have turned their backs on God. The proud are not merely unpleasant individuals; they are the standing opposite of the humble people God favors, and their pride is treated as something close to the root of all sin, because it begins with turning away from God.