I would not shoot. This could be anyone! What if Rover has a batch of rabies?
Possibility Numero Uno: Your neighbor was attacked by Rover, who was salivating and mad from the illness. The neighbor chased the dog into your yard with his gun, right into the doggie door. Then he thought he saw the dog in your kid's bedroom because of an errant shadow moving across the window. He kicked down the door in a mad attempt to save a life, shooting the dog dead when he saw it again. Now he's trying to make sure you are okay.
The only problem is, your neighbor is a deaf-mute. He cannot hear your shouted warning, nor can he speak of his own accord. He can only open that door and ensure that you are safe...
This is far-fetched and rediculous, I know, but it is just one example of how crazy life can be. Stranger things have happened, right?
It is simply smarter to give it another second and hose the person once they are in the room. Your weapon will be more effective if it hits the Bad Guy directly anyway, versus through a door.
Possibility Numero Dos: The B.A.T.F. has gotten a No-Knock Search Warrant (or perhaps they are Bounty Hunters, also known as skip chasers, who don't need a warrant!) but has pegged the Bad Guy they are seeking as living in your house instead of the one next door.
They are in your house in a flash, but had not accounted for the heavier security doors, dual deadbolts, attack dog and lack of unbarred windows. This has slowed them down considerably, much to the Team Commander's dismay.
You shoot first, through the door, without having seen the obvious B.A.T.F. (or Bounty Hunters Intl.) logo on the Point Man's jacket. When the point man is knocked back by the 00 buck, badly injured but alive, he and the rest of the team open up.
Full auto fire rips through the room, killing you, your Wife AND Baby Bonnie in her crib across the room.
And why? A few seconds more and you would have begun a dialogue, possibly saving all your lives.
These are just a few of the thousands of possibilities...
I'm new here, BTW, so hello! I'm hailing from Glocktalk and Shooterstalk, glad to find yet another board-full of pro-gunners!