God is said to be immutable by classical theists. I've spent hours arguing that God exists and that one of his many attributes is immutability. Still, I'm often asked: if A moves B, then doesn't A necessarily move too? In other words, if God moves (changes) something, then doesn't that require that God also change? The answer is no, and for at least two reasons.
First, it is possible to change something by being an immutable object of desire. While logic does not stand in any causal relations (e.g. it doesn't act on anything), it does passively draw persons to itself. After all, all of us desire to have knowledge and to be reasonable, and logic is a necessary precondition of such rationality. Likewise, God can also change things passively. People are drawn to God, as the Supreme Good, because they themselves desire to be good. Yet, God doesn't have to do anything in order to bring about this change, much less change himself.
Secondly, nobody has ever been able to show a contradiction in the notion that God could immutably will one change at time-1 and another change at time-2. Thus, God does not change things by mere passivity, as logic does, but he changes things with an immutable will for different changes at different times.