To respond to several prevailing ideas at once:
Yay organization!
I'm not going to object to the first part of the argument, because it's true for a lot of people. A lot of kids taunt you and such, and were they to act in a similar way as adults, many players would probably decapitate them for their insolence on the spot. (I am a little alarmed at how willing people are to justify their lust for child murder in terms of how much they feel the children deserve to die, but that's just unsettling, not really an objection.) But why does no one talk about the sweet children? Like that little boy who gets picked on by Braid (Baird?) in Whiterun? Half of them talk about their dreams of inheriting the family business when they grow up, and how fun it is to work in the forge or whatever. They don't all kick your shins and run away.
It is certainly a problem that a child can serve as an immortal witness to your crimes, however. That's a good reason to want to kill kids and a good reason to allow it. Otherwise it creates a weird situation where the player character is a necromantic, daedric worshiping thief trying to assassinate a local shop owner, and he can't because the kid is nearby. There's no plausible character reason he wouldn't just kill them both so there are no witnesses, so the fact that the game won't allow it forces him to break character.
It is certainly a problem that a child can serve as an immortal witness to your crimes, however. That's a good reason to want to kill kids and a good reason to allow it. Otherwise it creates a weird situation where the player character is a necromantic, daedric worshiping thief trying to assassinate a local shop owner, and he can't because the kid is nearby. There's no plausible character reason he wouldn't just kill them both so there are no witnesses, so the fact that the game won't allow it forces him to break character.
This is the simplest objection to child killing to reject. This is a game that allows thievery, desecration of corpses, animal cruelty, and of course murder of almost any other variety. How the ability to kill children going to make this game offensive in a way that all this other stuff does not? I can literally grab a mace, walk down to the market, and decapitate an old lady right there. She was certainly as innocent and harmless and pointless to murder as any child, yet the ability to kill her does not weigh heavy on the conscience of the developers. It's strangely selective reasoning and I don't buy it.
The explanation for this is that Bethesda could be accused of creating a "child killing simulator." By the exact same logic, Bethesda can already be accused of creating an old lady killing simulator. Has it not been because people simply don't care about the elderly? Now, I know that people are capable of getting worked up over nonsense, but that's what we're for. We provide the good press and the responses to the bad press that allow thoughtful, reasonable games to be made. The capacity of pundits and talking heads to get angry about silly things they don't like didn't prevent them from including same sex marriage in game - why should this be any different?
Yay organization!