I wasn't particularly motivated to do a image search on murder or it's synonyms, so this'll be pretty straight forward.

As people who play video games, we kill a lot of things. An amazing number of things. Ridiculous, outlandish, made up numbers of things. There's always a reason, someone has to be a bad enough dude to save the president, but the number of things we destroy is inordinate. Corollary: We never kill, incapacitate, or otherwise harm children. Technically that's wrong, because I used the word 'never' and I'm sure there are a few exceptions, but the exceptions prove the rule. There's a list of things it's okay to hurt and that it's not, and that's almost silly.

This doesn't represent their popularity in games, but rather how compelling the reason is. 'Self-Defense' ranks fairly weakly, 'Save the world' ranks fairly highly. The reason the designers give you to kill reflects how motivated they feel you should be to do the killing. The less motivation you require the more acceptable the victim, and vice-versa.The list I have in my head, from top to bottom most acceptable to least, runs like this:

Non-Humanoids: Demons, aliens, what have you- stuff with an obviously not-human shape to them.
Zombies: Used less often now because of realistic gore, but human shaped and unfeeling.
Robots: The only reason they rank lower than zombies is because most everyone can think of a sympathetic robot character. Plus, it's my list.
UnHumans: Human at some point but no longer, augmented by tech or magic or mutation. Usually some manner of boss.
Nazis, terrorists: Any enemy human really, becoming much more common than in ages past. Almost exclusively men, unless it's not.
Woomen: Get their own category simply due to their infrequency of appearance. More common in fantasy settings.
Children: Almost never a target.

Example:
You are the Wanderer, one of the few human survivors of a nuclear attack. What little humanity remains have mostly settled down, but here and there packs of bandits roam trying to profit from those foolish or desperate enough to wander the wastes. You are able to hold your own against these bandits and even free some prisoners, But wait! You come across a group of child bandits, far tougher than any adult because they're kids and you're not allowed to shoot them.

Wait, what?

I understand the external logic: It's not a very good idea to make the killing of children in any capacity a feature of your game. But internally it makes no sense: If those kids are out being raiders, you ought to be able to treat them as raiders. If they are neither friend nor foe, and not stage decoration in a town, why include them? And if they are random NPCs in a game world where I can shoot and kill damn near any person why exclude this particular group? Do I have a reason, some baby I lost and now have no idea what he looks like? Or is this to avoid recrimination? I'd rather the game exclude children entirely rather than make them a special case.

I'm not asking to be able to kill a baby, and I don't think many people would. I just think it's silly to create a situation where the only tool you're given is violence and then set restrictions on where you can use that tool. To mangle a quote: When the only tool you have is a gun every problem looks like a target. To set arbitrary restrictions on what is or isn't a target gets to be frustrating after a time. Make up an excuse: The children are kept safe in a special location until they are old enough to help with important tasks. We send our children away to a special school. Every child is taken away by the God-King so that he may find a suitable heir, the rest are trained from childhood to be citizens or soldiers. The children all ran off, and we don't know where they went. But they're not here, and you can't kill them.