"Because one (1) can be different from another one (1)."
In nature one can never be equal to another one. Therefore 1+1 = 2 is never valid. It is valid only for real numbers.
In nature everything is like apples and oranges. They cannot be added. Even two apples cannot be added, because they are different.
In math 1+1=2, this two is a single item on the real line. It is called closed under addition operation. When you add two objects from nature, they never produce another single object.
You cannot describe any property of any object of nature using mathematics. You cannot describe even an electron. If you isolate an electron from its environment then it will never remain an electron. It is just like taking earth out of its orbit. If you do that the earth will completely change. All people will die. The atmosphere will vanish. Same thing will happen to an electron also.