Thus, if someone sticks a gun in your face and demands your wallet, you should hand it over without hesitation—and run.
That depends; statistics say those who resist violent crime have better outcomes. It's something you should play by ear rather than blindly follow the above advice, the statistics are undoubtedly biased by people resisting when it makes sense.
Even if you are at home, in possession of a firearm, and well trained to use it, when confronted by an intruder your best defense is to get out of the house as quickly as possible. In such a circumstance, a gun is a means of ensuring that no one can block your exit.
This above is very iffy advice. Not only do you have much stronger legal protections inside your house, you're likely to have much greater control over the situation, and control is perhaps his main message. You know your house, can benefit from concealment and maybe even cover (that which a bullet cannot penetrate), you don't know the situation outside the house. You might escape only to be surprised by an armed accomplice. Or suppose you do this just as the police arrive; more than a few armed homeowners have gotten shot by police mistaking them for criminals.
You also need to balance this advice about decreasing the risk to your physical skin with the psychological toll fleeing takes.
Nothing good ever comes to people who allow themselves to be moved to a remote location at the mercy of a violent predator.
In my Missouri concealed carry class they ran us through a simulator with police "shoot/don't shoot" scenarios. For mine, I would have been a lot more aggressive and would have tried to shoot at various times if I'd know the terrible statistics of the above which the instructor mentioned after it.
As for his advice to flee and leave your spouse or children to the tender mercies of someone who, as he notes, has demonstrated he wants more than your property, if you have any other option I don't want to know you. That includes your being in such a situation because you decided not to procure one or more firearms prior to the incident.
After I left home, I only procured firearms after I had a significant other to protect, or vice versa. At that point it was an obligation, no matter what obstacles Massachusetts put in place (which aren't really that bad for long guns, although that may be changing depending on the city you live in).
On the other hand, I picked up a very hard rule about hostages from Jerry Pournelle in The Mote in God's Eye: at that point, you mentally treat the situation as if the criminal has killed the hostages, even if you then try to rescue them. In this situation, as the author says, you don't increase the toll by submitting yourself as well. The odds are very high that will make the situation worse.
Final note, underlying a lot of what he says: if someone unknown knocks on the door, I don't answer without having a gun in my hand. If I'm expecting someone, I confirm it's them before opening the door. Or per a rule of Marine general James Mattis WRT to being in Iraq or Afghanistan during our recent unpleasantness, which addresses even more points the author made: "Be polite, be professional, but have a plan to kill everybody you meet."
Couldn't agree more about leaving your family to an intruder. By all means call the police, and by all means stand and fight.
As for defending the family, going back to frontier times we're not that sexist, e.g. my father taught me and all my siblings how to hunt, fish, shoot and drive, and my younger sister still schools "the boys" when her husband and friends go skeet shooting.
Holy crap. Do we live on the same planet? Being murdered by an unknown assailant who knocks on my door is so far down my list of risks and fears that it doesn't even register. I'm far more worried about being hit by a bus as I cross the street, or my car spontaneously catching fire in my garage. Sure, it could happen, but so could a meteor that obliterates my house, and it hardly seems worth any effort.
I carry daily, but generally don't have a firearm on my person when I'm at home. That said, my front door is down a flight of stairs, and there is a rifle just out of sight at the top fo the stairs.
As for the odds of needing it... well, they're obviously quite low. I live in a low-crime area and a large portion of my income goes to ensuring that is the case. Even so, my town (Charlottesville, VA) is currently in the national news because a college girl was abducted off the street about a block from my office. There have also been a handful of home invasion robberies in nearby towns over the past couple of months.
It seems extremely reasonable to at least have the option of using an effective weapon to defend one's self.
"Any" effort? You admit the risk is non-zero (and it's certainly a lot greater than that meteor), for me the effort is rather low, since I keep that gun handy for whenever I go outside and carry it concealed.
Let's add an additional dimension: this precaution is so easy it would be downright embarrassing to not take it and then get bushwacked.
I'd like to think the risk of killing an innocent is negligible. I'm neither morally or legally allowed to use lethal force unless I (technically a "reasonable person" https://en.wikipedia.org/wiki/Reasonable_person) believe I'm being threatened with lethal force and that's the best option.
My above testimony should be ample evidence that I realize the terrible responsibilities and consequences of using lethal force; I am therefore necessarily hesitant to do so, specifically my threshold is set high to avoid ambiguity. In my case, not having any dependents, and living with someone who's also capable of defending himself, I'm willing to take a certain degree of risk to avoid using lethal force on an innocent.
In this vague hypothetical, I might instead retreat into my house, perhaps warning the possible assailant that I'm armed and don't want to have to shoot him. Someone who (continues to) advance in the face of that (not to mention entering a dwelling with a strong anti-invitation) could be judged a threat.
Although not necessarily a lethal one, but if someone continues to advance on a visibly armed man, the man can at some point presume the one advancing intends to take the gun away, thereby posing a lethal threat. And all this leaves out whatever that person is saying, all part of his demeanor which one uses in judging his intent.
Isn't this a little disingenuous? "Robbed" includes you being pickpocketed, or someone stealing your TV from your apartment while you're at work. If you're going to be raped or murdered, it's most likely not going to be a predator that does it, but someone you know. What's the probability that you will experience violence at the hands of a stranger? That is the relevant statistic
If you're just being robbed, you just give them your money; but if you're about to be raped and/or kidnapped, this could quite possibly save your life.