From the utilitarian standpoint, one has to answer two questions if you are going to allow passengers to defend themselves on board. The first is who will be allowed effective self defense, and the second is what weapons will be allowed?
The problem can be simplified if we take firearms out of the equation for the moment. Let's use edged weapons as an example, since no one is alleging that a knife could depressurize the cabin, under any circumstances. And, an edged weapon is a terribly effective defenive tool -- so effective, in fact that the only safe defense against it is a firearm used outside of the attacker's reach. But I digress.
Let's consider question 1 for a moment: who is to be permitted the means of defending himself? Well, following the previous poster's line of reasoning, the person's mental equilibrium should be assessed. Also, any temporary imparement (emotional, or chemical, or otherwise) needs to be factored in. Also, the skill level of the defender would want to be assessed, so that an innocent bystander is not injured by the defender. (Let's assume that one is free to disregard one's own safety in meeting an in-air attack. In fact, at the moment, we're forced to.)
This is not an overly daunting task. There are literally thousands of LE agencies in this country that undertake psychological screening of potential personell, offering a model for either private enterprise (my choice) or the federal government to pre-qualify potential armed citizens. (remember, we're not talking about guns, here.) With regard to the technical skill required, this is much more demanding for edged weapons than firearms, but again, training in the used and defense against edged weapons is available in every American city large enough to support a karate studio. So, off the top of one's head, there could be a two-tier process: pass the psych. profile (and citizenship requirements), then get certified as technically competent with the weapon. So, still opposed? If so, you can't really be worried about depressurizing the plane, you must be worried about something else. What is it? That your fellow citizens would go berzerk and start hurting people? Remember, there are a dozen or so other trained people are on board too. Worried about the safety of the "defender", well, me too. Edged weapons favor the young, the fit, and the highly (I mean every day) trained. So let's move on to point 2) what weapons would be allowed?
We've talked about edged weapons above, and I've touched on some of the problems there. What about handguns? It is true that frangible rounds are available that pretty much won't go past their target (as long as you hit it), but those will still perforate the cabin wall of an airliner. Don't beleive me, go check the ballistics. Also, some manufacturers of self-defense ammunition are a bit twitchy about .45 caliber rounds stopping in the target. So, we will probably want to restrict the caliber of the gun, and the type of ammunition. How do you do this? It's much tougher to allow only some items past a cordon that to restrict all of them, but it's not impossible. The notion of issuing ammunition and matching guns to pre-screened passengers is worth looking at carefully. So is the notion that the hand baggage and firearms could be screened, perhaps in a separate area, by a group of trained guards. The permit holders would also be strongly incentivized to screen themselves.
This is getting a bit long, but it strikes me that the argumetn against allowing at least some passengers to carry, is rooted in the false notion that the alternative is presumptively safe . On the contrary, I would argue that the present policy is both insanely dangerous, and has proven to be catastrophically wrong, on more than one occasion. Now, we are faced with the fact that our own government has simultaneously told us that the air force is authorized to shoot down cililian airliners that are deemed to pose a threat to ground-based buildings or other targets, while we are denied the means of effective self-defense in the air. This is stupid as a practical matter, and morally reprehensible.