Perhaps a good way to demonstrate such incredulity is to make a creationist-like statement. When creationists say things like "how can you have a watch without a watchmaker" it offers an insight into the kind of thinking which points to the incredulity. Some are no doubt better than others, the watchmaker argument is much better than incredulity expressed in "how can chance produce an eye?" or "have you ever seen a dog give birth to a cat?" But at least there's a means to explain why such arguments fail, even if the creationist might not be receptive to correcting that misunderstanding.
So here is my creationist-like incredulity at classic theism:
How can you have agency without an agent?While I think the statement is self-explanatory, I feel it deserves a little more explanation. The notion of agency is something I feel central to the belief in God. We are told that God hears prayers, heals the sick, watches over us, empathises with us, knows our beliefs, creates order in nature, etc. In other words, God as is described is what we understand as an agent. How can something experience empathy if it has no experience? What does it even mean for an abstract to be omniscient? To know implies cognition, an abstract cannot have cognition as cognition necessitates experience.
There's no point in praying to an abstract any more than there is to gravity. There's no point in worshipping an abstract any more than there is in worshipping pi. There's no point in saying that something has divine authorship, unless it is meant in the most diffuse sense - in the same way as describing the big bang as causing authorship. And there's certainly no point in making arguments to design any more than crediting the idea of a unicorn as a designer.
I can't see how a classical theist could even possibly hope to reconcile anything that makes God worthy of the concept with what they profess to believe in. The best I can gather is that it's a more philosophically-defensible position, a concept can be used as a grounding to any problem of regress, yet at the same time carry the cultural baggage that comes with the concept unchecked. Just start with existence being a necessary quality of maximal greatness and from there the sacrifice on the cross is defended on classical grounds.
I honestly don't think that there are many people who really are classical theists, but traditional theists - believing in some form of agency but that which is unlike (but analogous to) what we know as agency. That God has a mind, that God has the capacity to observe and interact, and that we can have a relationship with such an entity. I'm not sure if traditional theism is anywhere more coherent than classical theism, but at least it seems in line with the conception of what God is meant to be. Because describing an abstract with terms that only make sense to use on an intelligent agent seems as confused as describing God with the quality of carbonated, yet God is not a soft drink.