The number 42 is also a mathematical symbol we can observe. (Or two symbols, depending on how you want to define symbol).
You can observe the symbol. You can observe 42 of some object, 42 sheep for example.
You can observe a pie chart, or an actual pie, with 42% of it missing.
You can observe a plank of wood that is 42 inches or centimeters long.
But you can't observe 42 itself.
It is not like a hill on a map, where there is a symbol, and there's an actual hill.
It is an adjective and not a noun. It's not real unless it is describing something else.
My point being that regular finite numbers are not real either. So what's wrong with infinity? Or the square root of 2, or pi?
I actually agree, there's nothing wrong with infinity. I think finitists are silly and ultrafinitists are ultra silly.
Well importantly like scrubs points out in a sibling comment
42+1 = 43, 42 + 1 ≠ 42, ∞ + 1 = ∞
Infinity plays by very different rules than numbers.