> The proposition that infinity is "real"

As far as I can tell, numbers aren't real either. "Twelve" isn't a thing that exists in itself in the physical universe, it's an abstraction over some features of reality.

"Infinity" is another abstraction, but it's not the same kind of abstraction as "Twelve". It's a further step.

All mathematics is abstractions, layered on each other. See also "God created the integers, all else is the work of man"