The former is like saying "I won't wear seatbelts so I can get out of the car quickly in case of fire". The latter is saying "I'll buy a fire extinguisher for my car, but I'll keep it locked up under the hood."
Simply not true: https://www.google.com/#q=push+button+gun+safe (Americans are problem solvers, after all; you can also use one with a key and keep that on your person, say, on a string around your neck; this is also what hardening your entrances etc. is about, to give you time to react).
And "appropriately" is really situation specific; I haven't lived in a situation where there was danger of another abusing one of my guns for decades. There's also the pattern of keeping it in your safe until you get home (and if you're really hard core, carrying it until you go to bed). And you're completely ignoring concealed carry, which covers 42+ of the states and ~72% of the US population, 12+ million licensees, and 10 states without a license requirement: https://news.ycombinator.com/item?id=11980298
And that's before we even get into the "much more likely", which simply isn't supported by the facts, starting with a 25% drop in the number of fatal gun accidents per year in the period 1980 to now, while both the population and number of guns owned by it roughly increased by 50%.
Note that if you're depending on e.g. Kellerman's studies, they score only fatal outcomes for home intruders as successful defensive gun uses, when the majority don't involve any shots being fired, the vast majority don't involve anyone getting hit by a round, and pistol torso hits resulting in fatality only about 1/4 of the time. Even the biased CDC admits to the utility of guns: https://www.google.com/#q=%E2%80%9CSelf-defense+can+be+an+im...
Historian Joyce Lee Malcom has pointed out that a steady trend of declining interpersonal violence starting in the 13th Century reversed in a few decades. Others point out that "burglaries" in the U.K. much more frequently take place when dwellings are occupied than in the US. See the British Crime Survey, which as of 2009 said:
There were 284,427 burglaries.
20% of those were face to face.
In 59% of those cases, violence was threatened or used.
In 40% of those face to face encounters, violence was actually used against the householder, a rising number since such statistics were first collected in 2002-3.
If the subjects of the U.K. don't feel a need for guns for self-defense; maybe they aren't getting killed in large numbers, but they're getting brutalized, and that's very bad in a zillion ways.
The very definition of citizen, vs. subject or slave, is one who bears arms in defense of his polity.... (Although that's not something that Black Armband History mentions....)
Your "orders of magnitude" claim about school shootings is flatly WRT to Europe, especially Western Europe (which is significantly larger than the US in population), compare, for example, https://en.wikipedia.org/wiki/School_shooting#Europe and https://en.wikipedia.org/wiki/List_of_school_shootings_in_th... This is especially true about the ones of larger magnitude.
UK robbery incidences: 76,179 (THOSB – CEW page 61, paragraph 2.)
76,179 / 561 = 135.72
US robbery incidences: 354,396 (FBI – CUS)
354,396 / 3116 = 113.7
You are thus 1.1x (135.7 / 113.7) more likely to suffer robbery in the UK than in the US.
Now, robberies in the context of home invasions I don't know, and I didn't see it on that page. Nor did I see where you then got a 4x more likely to be killed if in a house invasion robbery in the US, although I'm quite willing to believe it. But I'll seriously look at that page, the author's inclusion of BCS and NCVS statistics means he's serious (as, e.g., a posting in the current "Dial 911 and get Wall Street" topic notes, US robbery statistics are understated by cities where they don't even bother with them if there's no injury).