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That's a nicely unfalsifiable bit of bulverism you've got there. I think I agree that "no rational argument would probably do", but we may not mean the same thing by that.
[EDITED to add: I see no particular problem with the use of infinities in mathematics and never have; back when I was religious, I saw the mathematical notion of infinity as clashing a little with my notion of God -- because in mathematics there is e.g. no all-surpassing maximal infinity -- and I don't recall ever, as theist or as atheist, "loving infinity deeply and strongly" or seeing mathematical notions of infinity as doing anything to create or fill "spiritual emptiness". Of course introspection is unreliable, but it's all I've got :-).]
I was always an non-spiritual atheist. (But I am a non-progressive, too,)
It may seems a bit naive, but when I have heard (as a child) about that paradox about omnipotent god who can't create a rock so heavy that even he couldn't lift ... then I suddenly "knew" that quantities too big are (logically) problematic. Let alone infinite quantities.
Today, Yablo's paradox is already good enough for me, to convince me that the infinity doesn't work. How everybody doesn't agree with me about this - baffles me.