Think about this scenario and a question. Someone drives his car up over the curb into your yard to hit one of your children. Will that affect your relationship with the driver? Will this tend towards closeness with him? Cutting off associations with people is the God-ordained means to protect you, your family, your present associates, and what you believe. If their behavior dishonors God, you will honor God through the separation as well. Honoring God also alligns us with God's protection. When people do not separate, normally this occurs because they don't take the matter too seriously. It's easy to disassociate from someone who runs over children, because that bothers us personally. However, are we willing to trust God enough to separate over something that He said? When we treat someone who continues to disobey God's Word as if he has done nothing wrong, this tells God something about what we think of Him.
Truth by nature is antithetical. You can't love truth and error simultaneously. Loving truth requires rejecting error. Loving health mandates hating disease. Loving right doctrine means hating false doctrine. We can't both love and hate false doctrine at the same time. To get rid of false doctrine and practice, we must treat them like they matter to someone, at least to God, and hopefully us. Consider these words from David in Psalm 139:21, 22, "Do not I hate them, O LORD, that hate thee? and am not I grieved with those that rise up against thee? I hate them with perfect hatred: I count them mine enemies." David had a loyalty to God that necessitated hating them which hated God. David also wrote in Psalm 101:3, "I will set no wicked thing before mine eyes: I hate the work of them that turn aside; it shall not cleave to me." People today behave as if they are more loving because they tolerate all sorts of behavior. They surely do not love God more, and if they love God less, they surely cannot love people more.
Truth is distorted by error. The only way to protect truth is to keep it separated from falsehood. We must separate over wrong doctrine and practice. If we don't separate, we will not properly represent the truth. We will make the error as if it did not matter. We will be an accessory to the destruction of the truth.