If God is love how can He hate?

The Bible clearly states that God is love, loves people, and wants us to love in the same way that He showed us love on the Cross. However, the Bible also states that God hates sins such as lyring, pride, divorce, etc. So how can someone who is 100% love, have any particle of hate in Himself?

Here is my take, which I pray is Spirit-directed. It came to me just this morning:

It's simple. God is love; so wherever God is, there Love abides as well. God does NOT dwell in evil things ... no part of Him is in blasphemy, cruelty, and lies. Those things are full of satan and evil spirits, and by nature, have no Love in them. Therefore, if you take away love, you are left with hate. If God is not in them, He does not love them.