This is a good point and I agree with the premise that Christians do not fight at all, but there is a way in which the one who would embrace fighting as a Christian virtue could counter this.
First it necessary to understand that a "minister" of God does not mean that the person is saved or worships God, it only means that God has corralled him to do His will. God uses many people to do His will and they are all His ministers. Nebuchadnezzar was God's minister and was defeated by Cyrus who was also God's minister. I think the real question should be, "How can one Christian justify killing his brother Christian in a war where both governments employ Christians as soldiers?" The answer is, that Christians should not be in the ranks as soldiers. Personally, I do not think he should serve even as a non-combatant, but that is a different argument.
War and fighting belong to the world of darkness, 1 John 2:7-11. True believers have passed out of the darkness of the world into the light of understanding, which Light was exhibited by our Lord.