Infinity minus an infinity yields logically impossible scenarios. Notably, one can take away identical quantities from identical quantities and arrive at contradictory remainders.1 This is relevant because if an infinity could be instantiated in the real world, then so too could these contradictions. (But in fact, contradictions can’t be instantiated, and so modus tollens infinities can’t either.)
Infinities yield metaphysically impossible scenarios (absurdities)
• …the infinite-room hotel.
• …the infinite rainbow popsicle.
A part of the whole contains less than the whole (i.e. In reality, if M’ is a submultitude of M, then intuitively there are more things in M than M’). This is relevant because if infinities are possibly instantiated in the real world, then this intuitive proposition about the world is actually false.
“The notion of an 'actual infinity' is logically consistent/possible within Axiomatized Set Theory.”
But, so what? A concept's being logically possible (free of formal contradictions) doesn't entail that it is actually/metaphysically possible.1
Any interval contains an infinity of subintervals (e.g. a meter and minute can both be divided in half an infinity of times).1, 2 This is relevant because if there are an infinity of sub-intervals inside any interval, then an actual infinity of subintervals must exist.
God is an infinite being. This is relevant because if God is an infinite being, then God's existence entails the existence of an actual infinity.
The extent of God's knowledge would be infinite (given God exists and is omniscient). So if actual infinities are impossible so is God.1