You shall not hate your brother in your heart, but you shall reason frankly with your neighbor, lest you incur sin because of him. You shall not take vengeance or bear a grudge against the sons of your own people, but you shall love your neighbor as yourself: I am the LORD.
There are three insights into social relationships that I think are interesting to talk about from this passage. The first has to do with the words that are used to describe relationships with other people. The concepts of brother and neighbor are used interchangeably in this context. I think the idea is that my obligations to other people are closer than I think. Of course I may be tempted to deal more fairly with a family member than with a stranger, and the point is I must apply myself in relationship with both. I cannot hate my brother. I should not sin against my neighbor.
The second insight is that sins on the social scale affect my walk with God. If I am not right with other people due to wrongs I have done to others, I am not right with God. The warning against striking out against brother or neighbor points out that sin will result. And this is just after a LENGTHY section of Leviticus has detailed the multitude of sacrifices meant to deal with sin issues. The point is not missed. Any sin is a serious matter. God sees sins against people as sins against Him as well. As a counselor, I often have to help people deal with the effects of how the hurt they have put on others has hurt their relationship with God. They have also hurt themselves. This is true stuff.
The third insight is the role of love. It is what defines our relationships with others. Since I would not hate myself, I should not hate my neighbor. Since I love and serve God, I should love and care for my neighbor. And Jesus made it clear that any person is my neighbor when He told the tale of the Good Samaritan. Jesus was bold enough to say that love defined the true two great commandments. The first was to love God. The second was to love my neighbor as myself. So this is no light obligation or minor suggestion. It defines the heart of all my relationships.