Well, the fact that the kid went for a gun instead of a readily accessible knife is either because the gun is even more readily accessible than the knife or that guns are much preferred when it comes to performing a murder.

In the latter, the kid might've decided that the hard parts of murdering his father might not be worth dealing with if he doesn't have easy enough access to the gun in the first place. So the question goes back to why it was so easy for an 11 year old to get his hand on a gun in the first place.