I hate this phrase. "Hate the sin and love the sinner". God does not do this. It simply aint in the book.
Rather, we read: Psalm 5:4-6 (New International Version)
4 You are not a God who takes pleasure in evil;
with you the wicked cannot dwell.
5 The arrogant cannot stand in your presence;
you hate all who do wrong.
6 You destroy those who tell lies;
bloodthirsty and deceitful men
the LORD abhors.
Apparently God hates the sin AND the sinner. This is his justice, his righteousness.
So then how do we square this with John 3:16? "For God so loved the world..." (assuming the world is full of those who "do wrong").
The answer, my friends, is found in the paradox of Law and Gospel. The Lord who hates sins AND sinners also LOVES sinners - so much that he sends his own Son to save us. This is a deep mystery.
But God will not angrily send people's SINS to hell. He will send sinners. He does not separate sins from sinners except in Christ. So, I suppose for the Christian, our little catch phrase might apply better - but I am always wary of this type of sound-byte theology. Too much wiggle room here for false theology.