In prison, Paul converted a runaway slave, Onesimus (Phlm 10). This made Onesimus a son of God, Paul's brother in Christ, in addition to the Christian brother of Philemon, Onesimus' owner, who was also a Christian.
When we realize that others are our brothers and sisters in Christ, this should dramatically impact our relationships with them. For example, Christian brotherhood and sisterhood eventually undermined the deeply ingrained social institution of slavery. For how could we enslave our brothers and sisters in Christ? Christian brotherhood could have prevented the World Wars. For how could German brothers kill their Russian, French, or Polish brothers in Christ? How could we drop an atom bomb on our brethren in Nagasaki? If we saw other Christians as our Christian brothers and sisters, we would not tolerate centuries of denominationalism in explicit contradiction to God's will (see Jn 17:21; Jn 11:51-52). How could brothers and sisters in Christ live in luxury while our "brethren" are starving to death?
The realization of our baptismal brotherhood and sisterhood is meant to transform our world, social institutions, lifestyle, economy, and Church. Finally, because of the exceptional importance of Christian brotherhood and sisterhood, we will be judged on Judgment Day on our practical love for the brethren, our Christian brothers and sisters (Mt 25:40).