Does love exist?
Are you talking about the warm scrummy emotion that people get, when they hug teddy bears, or the action that people do, when they have cared for someone for a long time?
There are 2 parts to "love": the emotion, and the action.
If God loves us, then he has that warm scrummy feeling, when he tortures us.
If he feels responsibility towards us, then it's a broader type of responsibility that only cares about his own objectives.
God might love us in a broader sense, but it's only speculation.
Christians like to pretend that God is teaching us lessons, because the universe teaches us lots of lessons. If it didn't then we wouldn't need a brain, or need to adapt. Any form of adaptation or learning can be explained as in response to God's "love". If a monkey falls off a tree, and breaks its spine, then God taught it a lesson out of love. Everything must be "love", because then otherwise God is hate.