not addicted to wine or pugnacious, but gentle, peaceable, free from the love of money.
1 Timothy 3:3

For the overseer must be above reproach as God’s steward, not self-willed, not quick-tempered, not addicted to wine, not pugnacious, not fond of sordid gain…
Titus 1:7
(emphases mine)

Pugnacious can be defined as one who is cruel, brutal or a bully. It can also refer to a contentious person or one given to quarreling.

It is easy to understand why this characteristic would be unacceptable for an elder. After all, elders are biblically required to work together harmoniously. If an elder is inclined to demand his own way or if he works behind the scenes to manipulate others to concede to his preferences, he is not qualified to serve in this office.

Therefore if there is any encouragement in Christ, if there is any consolation of love, if there is any fellowship of the Spirit, if any affection and compassion, make my joy complete by being of the same mind, maintaining the same love, united in spirit, intent on one purpose.
Philippians 2:1–2

Elders also must deal with difficult situations in the life of the church. It is essential that they are able to do this in a way that is pleasing to the Lord. They must not be harsh, unloving, impatient, or overbearing. Consider the testimony of the apostle Paul:

But we proved to be gentle among you, as a nursing mother tenderly cares for her own children. Having so fond an affection for you, we were well-pleased to impart to you not only the gospel of God but also our own lives, because you had become very dear to us. For you recall, brethren, our labor and hardship, how working night and day so as not to be a burden to any of you, we proclaimed to you the gospel of God. You are witnesses, and so is God, how devoutly and uprightly and blamelessly we behaved toward you believers; just as you know how we were exhorting and encouraging and imploring each one of you as a father would his own children, so that you would walk in a manner worthy of the God who calls you into His own kingdom and glory.
1 Thessalonians 2:7–12