Hatred is the direct opposite of love. Merriam-Webster's Dictionary defines hatred as "extreme dislike or disgust". That is how God sees sin. He hates sin. It disgusts Him. It goes against His character. The psalmist wrote "for thou art not a God that hath pleasure in wickedness: neither shall evil dwell with Thee" (Psalm 5:4). God also despises sin because it is what separates us from Him. Isaiah the prophet said in Isaiah 59:2 that "your iniquities have separated between you and your God, and your sins have hid His face from you, that He will not hear". Hatred itself is not a sin for we are called to hate evil (Psalm 97:10). It is where our hatred is directed that turns it into a sin. "If a man say, I love God, and hateth his brother, he is a liar: for he that loveth not his brother whom he hath seen, how can he love God whom he hath not seen?" - 1 John 4:20
If a Christian hates another Christian, it causes division. If a Christian hates a non-Christian, it ruins their testimony. The Apostle John said that God is quick to forgive our sins if we ask for forgiveness (1 John 1:9, 2:1). Yet, if we hate one another, then we are not showcasing the kind of love that we are told to display. In 2 Corinthians, the Apostle Paul said "now then we are ambassadors for Christ, as though God did beseech you by us: we pray you in Christ's stead, be ye reconciled to God" (5:20).
We are His ambassadors! We are to show His love towards each other and towards those that have not accepted Jesus as their Lord and Savior. When a person is doing wrong, we are not to attack them as many denominations and cults do (Westboro Baptists for example). We are to show love. Love does NOT mean acceptance though. What Jesus did on the cross proves that. In Romans 5:8, the Apostle Paul wrote "but God commendeth His love toward us, in that, while we were yet sinners, Christ died for us". Love changes people and overcomes sin while hatred intensifies sin. Paul also said "what will ye? shall I come unto you with a rod, or in love, and in the spirit of meekness?" (1 Cor. 4:21).
"Hatred stirreth up strifes: but love covereth all sins." - Proverbs 10:12
Next work of the flesh: variance