It seems to me that in the background of his criticism of your logic, there lurks an unstated premise/conclusion (not sure which) that Jesus could be God ONLY if Mary were immaculately conceived, which I think would be absurd.
Am I reading this correctly? The disclaimer here is that I do not possess a Ph.D. in Philosophy or Logic.
I think it always gets us in trouble to try to use hypothesis contrary to fact (or, in this case, to dogma) because you can't change one thing without opening up changes to all the other things. "Suppose God had Not done such and such ...." well how many other things would He have done or not done?
In the Narnia books Aslan always rebuffs questions about what might have been.
I think the significant item in the objection is the assumption that our arguments are intentionally specious, in the sense of falsely attractive. And that's significant not only because it reveals the cultural suspicion that ALL of Catholicism is wily but because it implicitly accepts the contention of both Freud and Marx that pure reason is really non-existent or that, if it exists, it is not authoritative. An argument cannot stand, it seems to be thought, if it turns out there is some hidden motive.
Consider this! If I say All man are mortal; Socrates is a man, therefore Socrates is mortal, the validity of that is held to depend on my sincerity and candor! I think whether I wish Socrates dead or wish he could live forever, the Argument stands.