This is the argument I call the "Rabid Dog Fallacy", a variant of the fallacy of false dillema or the fallacy of complex question. As background, here's the Fallacy of False Dilemma, from Stephen's Guide to the Logical Fallacies:
A limited number of options (usually two) is given, while in reality there are more options. A false dilemma is an illegitimate use of the "or" operator.
Putting issues or opinions into "black or white" terms is a common instance of this fallacy.
Identify the options given and show (with an example) that there is an additional option.
And here's the Fallacy of the Complex Question:
Two otherwise unrelated points are conjoined and treated as a single proposition. The reader is expected to accept or reject both together, when in reality one is acceptable while the other is not. A complex question is an illegitimate use of the "and" operator.
Identify the two propositions illegitimately conjoined and show that believing one does not mean that you have to believe the other.
They are like the Fallacy of Complex Question because the "two otherwise unrelated points" ("to have an immediate defense", and "to try to prevent the threat from occuring in the first place") are treated as a single proposition that we are expected to accept or reject. To show this is a fallacy, I only have to show that the two propositions are illegitimately conjoined and that you can believe one but not the other, namely: that it is possible to support both immediate defense and trying to prevent more from being created.
In the case of both rabid dogs and rapists, removing the primary causes for rabies or the motivations for rape would probably significantly reduce the number of occurances of both. But even with the main causes taken care of, there are still freak or "natural" occurances. Rabies exists in the wild, and can be caught by domestic animals. Some people are evil, or sick, or have bad brain chemistry, and they will still rape.
Because these threats can still occur, a prudent person will take precautions so she can defend herself against rabid dogs and/or rapists, even when those problems are being addressed systematically. To remove her right to defend herself, or the tools to do so, is immoral because the right to self-defense always exists.
So please quit with the "Rabid Dog Fallacy" already.