God being impassible is probably the most rejected and misunderstood attribute of God. In fact, it’s usually rejected probably because it is so misunderstood.
But first, what does impassible mean? Well in the broadest sense it means, “not able to suffer”.
When one thinks about the concept of God as Omnipotent, Infinite, and so on; it seems bizarre (in one sense) that the attribute of impassibility is so often rejected. On the other hand it’s not that weird that some people have trouble accepting this attribute in regards to Jesus dying on the cross. However, if one doesn’t accept that God is Impassible because of the Incarnation/life of Jesus, then one is seriously misunderstanding the doctrine of impassibility.
Jesus suffered and died in his human nature, not His divine nature. In fact, I don’t know how it’s possible for the God of classical theism to suffer in His divine nature. (Maybe it is possible for the God of neo-theism/theistic personalism. Sometimes the God of theistic personalism can look like a super-duper hero or Zeus). Since Jesus suffered in his human nature, it makes no sense to say that, “God suffered”, anymore then it makes sense to square a circle. At best it can be misleading or ignorant to say, “God died” or “God was crucified”, without further elaborating what you mean. Given God’s divine nature, it’s impossible for God to “bleed” or “die on a cross”.
Furthermore, D.A. Carson argues that we can still maintain the doctrine of impassibility by making just one qualification (we make qualifications all the time when discussing the attributes of God i.e. Omnipotence-God can do anything if and only if said thing is logically possible). Carson says God can’t suffer, unless God chooses to do so like in Jesus.