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Pastors are called and trained to fight. The type of fight is different fight. This is not a physical fight though it includes the physical world. This is not a argumentative or quarreling fight though it includes arguments and courageous "holding fast" to truth and love. They are led to fight for and against something, rather, someone. The "noble task" Paul tells Timothy is difficult because the world is broken and the pastoring people is not easy. Therefore, this is a unique fight that Paul commands the young pastor Timothy to do, "Fight the good fight of faith (1 Timothy 6:12)."
Fight
Paul trains Timothy:
But as for you, O man of God, flee these things. Pursue righteousness, godliness, faith, love, steadfastness, gentleness. Fight the good fight of the faith. Take hold of the eternal life to which you were called and about which you made the good confession in the presence of many witnesses. I charge you in the presence of God, who gives life to all things, and of Christ Jesus, who in his testimony before Pontius Pilate made the good confession, to keep the commandment unstained and free from reproach until the appearing of our Lord Jesus Christ, which he will display at the proper time—he who is the blessed and only Sovereign, the King of kings and Lord of lords, who alone has immortality, who dwells in unapproachable light, whom no one has ever seen or can see. To him be honor and eternal dominion. Amen. -- 1 Timothy 6:11–16 ESV
Paul used the previous chapters and verses in 1 Timothy 1-6 teaching and commanding about various issues in dealing with God, people, government, and society, and his overall command is then to get away from what other pastors and Christians along with the surrounding community of people were falling into (a love for themselves vs. a love God). Many pastors were falling specifically into the love of money and pastoring people to that end (cf. 1 Timothy 6:9-10). So then Paul summarizes with a command in a way of getting away from all of that and pursue what God wants and fight for that. This is part of why Paul started the letter to Timothy with another key verse of "the aim (telos) of our charge is love that issues from a pure heart and a good conscience and a sincere faith (1 Timothy 1:5)."
Therefore, in order for a pastor to know what he's fighting for, he must have a 'sincere faith' in God, specifically in Christ and Christ alone. When God then is the epicenter of his life, any pastor is able to courageously "fight the good fight of faith." Through God comes clarity to understand that this world is broken, imperfect, evil, and filled with a spiritual warfare many times unseen working itself out in real life.
Fight then is a command including great imagery of a fighter entering a contest working through struggles, setbacks, difficulties, hardships, pains, discouraging factors, and against a powerful opponent. The greatest issue for any fighters tends not to be the strength of one physically or motivationally, but rather, the strength of what then motivates the heart (outside-in) to be steadfastly struggling through the pain to achieve a reward greater and humbler than pride, position, perception, power, money, prestige, or comfort affords. A pastor's strength then is not found within but found outside of him (God and the gospel) working inside of him ("pure heart and good conscience").
For pastors, we fight to the death because we have life in Christ. Another way to say it is that pastors live a lifestyle with an aim set on God and characterized by Him to love (spiritually, truthfully, and humbly) regardless of threat of death (spiritually, physically, financially, relationally, or emotionally). Pastors feel the pains and occur the losses but live beloved by God to love Him and others. Pastors listen to our commander in chief, Christ, to fulfill the noble task set before us which is to lead people to fight the same fight of faith -- living for Christ in real life with him as the epicenter of our hearts for others to taste of his goodness and gospel.
Pastors then are fighting to follow Christ and his command to train people to trust Christ with the entirety of their hearts and lives in real life.