In terms of just the straightforward even/odd thing it's just a handy way to split the integers into two groups. There's a lot* of ways of doing this, of course. E.g., prime and nonprime.
Superficially even numbers are not more "special" than odd numbers. It turns out that a lot of theorems are going to mention "even" somewhere along the way than they do "odd".
It's like how we use the "prime" a lot more than we use "nonprime"/"composite". We're not trying to use one over the other.
That's just the way Math rolls. Some properties gets used/referred to more than others. It's an inherent property of these systems.
And if you're talking my field, Computer Science, evenness is inherently built into the base of the thing. It all comes down to 2s.
* Understatement of the megamillennium.
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