Why is the difference of 2 odd numbers always even?

All odd numbers have an even number on either side of them. All even numbers are divisible by 2. So all odd numbers can be represented by the expression 2x+1 where x is any integer. Let another odd number be 2y+1.
Now subtract one from the other: 2(x-y), the ones cancel out. No matter what x and y are, their difference is doubled, making it even, therefore the difference between two odd numbers is always even.