God hates sin because it is contrary to His perfect and holy nature. It is impossible for God to do anything wrong. He cannot lie. He cannot cheat us. He cannot misrepresent the truth. Therefore we can see that holiness, which is the opposite of sin, is the standard as set by God Himself.
Sin causes separation between ourselves and God (Isaiah 59:2). Such separation has a horrible consequence: damnation. Therefore, God would hate anything that separates us from His perfect love and perfect standard of holiness.
Sin takes many forms. It can be aggressive as in rape and murder. It can be passive as when we do not do what is right and let others suffer. Sin can take the form of misrepresentation so that such things as adultery is called "an affair." Homosexuality is called "an alternative lifestyle," and abortion is called "the right to choose."
God must punish the sinner. If He did not, God would be approving of that which is contrary to His Holiness. God must deal with sin and; unfortunately for unbelievers, they will face the consequences of their sin if they do not trust in the person of Jesus Christ who removes the wrath of God from all who would believe and trust in Him.