Sometimes God allows what he hates to accomplish what he loves.
True, God hates Alzheimer's, spinal cord injury, mental illness, autism, and the rest (these conditions are all symptoms of the Fall). Yet he permits these things to accomplish something far more precious in our lives: patience, endurance, compassion for others who hurt, and refined faith and trust in God, to name a few.
God permits what He hates in order to accomplish something that He loves.
God cares most not about making us comfortable, but about teaching us to hate our transgressions and to grow up spiritually to love him.
Anyone who takes the Bible seriously agrees that God hates suffering. Jesus spent most of his time relieving it. But when being healed becomes the only goal - 'I'm not letting go until I get what I want' - it's a problem.