"Cull buck" and "meat buck" are terms used by those who can't kill big deer to make themselves feel better about settling for less.
Do you also use terms like "this is my ugly wife, she's not as good as the trophy wife I was going for, but someone had to jump on that grenade"?
What is so important about "big" deer?
Do you mean large antlers? You can't eat those.
If people are satisfied with a medium sized deer or even a spike buck if that's all they want, what's wrong with that?