Does God hate the sin but love the sinner? I've quoted a good response to this here and in that post referenced several others worth reading.
The video below is Greg Koukl addressing the point. He does an ok job, i.e., he responds better than I could yet I prefer some of the points made in the referenced links above. That said, I like how Koukl states "[God's] hatred is in virtue of man's rebellion and His love is gratuitous - it is in virtue of His favor and His grace. He is willing to apply His love against the hatred so that the justice that is the foundation that God has against sinners is satisfied by the self-sacrificial love that God provides through the work of the cross."