It is useless to give offerings to God while you are at enmity with your brother. Jesus said that His followers should be reconciled with anyone who has something against them. The world seeks reconciliation on limited terms. Christians are to be reconciled, whatever it takes.
You say, “But you don’t know how deeply he hurt me! It’s unreasonable to ask me to restore our relationship.” Or, “I tried but she would not be appeased.” Jesus did not include an exception clause for our reconciliation. If the person is an enemy, Jesus said to love him (Matt. 5:44). If he persecutes you, you are to pray for him (v. 44). If she publicly humiliates you, you are not to retaliate (v. 39). If someone takes advantage of you, you are to give even more than he asks (v. 41). The world preaches “Assert yourself.” Jesus taught, “Deny yourself.” The world warns that you will be constantly exploited. Jesus’ concern was not that His disciples be treated fairly but that they show unconditional love to others regardless of how they were treated. Men spat upon Jesus and nailed Him to a cross. His response was our model: “Father, forgive them, for they do not know what they do” (Luke 23:34).
If there were ever a command that is constantly disobeyed, it is this mandate to be reconciled. We comfort ourselves with the thought, “God knows that I tried to make things right, but my enemy refused.” God’s word does not say “Try to be reconciled,” but “Be reconciled.” Is there someone with whom you need to make peace? Then do what God tells you to do.