From Mere Orthodoxy:

Not a Rock – Critics often contend that the doctrine of impassibility depicts God as an emotionless rock. But to teach that God is impassible is not to deny that God has an emotional life with cares, joys, loves, and so forth. Impassibility does not mean impassivity any more than immutability means immobility. Both are caricatures and misunderstandings of the classical doctrine. Just as the doctrine of God’s immutability or changelessness is not a teaching about a static, stone God, but a God so perfectly overflowing with life that any “change” could only tend towards a lesser state, so the doctrine of impassibility is statement about the perfection of God’s emotional life, his sovereignty over it, rather than its absence. In the early Fathers, to teach that God was impassible was to teach that God did not have “passions”, or unrestrained feelings ungoverned by reason or will that could simply sweep over him. A passion was thought of as a sort of violent, semi-physical force that could move a person without the consent of their reason or will. To deny that this can happen is to say that God’s emotional life is under his own control and will not erupt violently in irrational or sinful ways. In other words, God is not an emotional teenager.