Yes and no. You are right that the definition of even-ness is how we determine whether zero is even or not (by that definition). But there are reasons to choo

Yes and no. You are right that the definition of even-ness is how we determine whether zero is even or not (by that definition). But there are reasons to choose one definition over another. Yes, you can choose to define zero to be exempt. But you can look at the patterns of numbers that are "obviously even" and observe that adding 2 to an even number results in an even number. So it's reasonable that subtracting 2 from an even number should result in an even number. That's not a definition, but it's a pattern to observe, and leads one to think that maybe defining zero to be even makes sense, and fits with existing patterns. You can define it how you like, but some definitions are more useful than others. That's why 1 is no longer considered to be prime, -1 is considered by some to be prime, and why even-ness is defined in such a way as to include zero. It creates fewer exceptions to general properties. It's more convenient, more useful, and simpler, than any of the alternatives. Patterns provide a reason to create the definition we use.