==Good news!== 

 I finally figured out your question, I've been thinking about it for the last year and a half.  You asked 

 ===Why?=== 
 The choice of even and odd seems arbitrary, I've never seen it explained anywhere. Could somebody explain the motivation for defining even and odd functions?   
 :Even when you divide in half you have mirror image on each side of divisor (so it equals itself).  Odd you're one man short which makes people sad.  To signify sadness/negativity, we use the minus sign.