1+1=2 is not really an axiom. There's a set of axioms that lead to that. They are even more primordial statements like "1 is a number" and "x=x" and "all numbers n have a successor number S(n) such that m=n if and only if S(m)=S(n)". Even if it seems clear (to most of us, at least) that these axioms represent some part of reality, they are still human-chosen -- and they have to be agreed upon. At some point, nearly everyone would have agreed that Euclid's 5th postulate was obviously true, and anyone alive could verify this for themself. Well, sometimes it's "true" and sometimes it isn't.

That said, the Peano axioms seem less nebulous that the varying axioms relating to the existence of god, as that concept can change so much from person to person.