Since there is no way to divide 1 by any natural numbers other than 1 itself, how can 1 be divided into pairs until either 0 or 1 units are left, letting us call it even or odd?
Perhaps the definition of odd numbers is irrational and wrong, at least for one.
Why is one considered an odd number?
I think an odd number is a number that when taking that number of units and dividing the units into pairs, you have either get an unpaired unit or not when you are finished. This definition does not include the number one. All natural numbers are testable except for one. A number must be able to be tested in this way before being called an odd number. 1 cannot be tested in this way, and therefore it cannot be called an odd number. The un-testability of the number of one makes it impossible to judge whether it is odd or even.