Arrogance is very similar to and sometimes is considered the same as pride which is condemned by the Bible.
For from within, out of the heart of man, come evil thoughts, fornication, theft, murder, adultery, coveting, wickedness, deceit, licentiousness, envy, slander, pride, foolishness.
(Mark 7:21-22 RSV)
For all that is in the world, the lust of the flesh and the lust of the eyes and the pride of life, is not of the Father but is of the world.
(1 John 2:16 RSV)
But understand this, that in the last days there will come times of stress. For men will be lovers of self, lovers of money, proud, arrogant, abusive, disobedient to their parents, ungrateful, unholy, inhuman, implacable, slanderers, profligates, fierce, haters of good, treacherous, reckless, swollen with conceit, lovers of pleasure rather than lovers of God, holding the form of religion but denying the power of it. Avoid such people.
(2 Timothy 3:1-5 RSV)
What causes wars, and what causes fightings among you? Is it not your passions that are at war in your members? You desire and do not have; so you kill. And you covet and cannot obtain; so you fight and wage war. You do not have, because you do not ask. You ask and do not receive, because you ask wrongly, to spend it on your passions. Unfaithful creatures! Do you not know that friendship with the world is enmity with God? Therefore whoever wishes to be a friend of the world makes himself an enemy of God. Or do you suppose it is in vain that the scripture says, "He yearns jealously over the spirit which he has made to dwell in us"? But he gives more grace; therefore it says, "God opposes the proud, but gives grace to the humble."
(James 4:1-6 RSV)
So I exhort the elders among you, as a fellow elder and a witness of the sufferings of Christ as well as a partaker in the glory that is to be revealed. Tend the flock of God that is your charge, not by constraint but willingly, not for shameful gain but eagerly, not as domineering over those in your charge but being examples to the flock. And when the chief Shepherd is manifested you will obtain the unfading crown of glory. Likewise you that are younger be subject to the elders. Clothe yourselves, all of you, with humility toward one another, for "God opposes the proud, but gives grace to the humble." Humble yourselves therefore under the mighty hand of God, that in due time he may exalt you.
(1 Peter 5:1-6 RSV)