The Texans see it like this: "Someday, somebody might attack me. The criminal is going to be armed one way or another. I want to be armed too so I can defend myself." The Europeans see it like this: "Why would somebody attack me? Society is basically made of reasonable people who are not violent to each other. If somebody starts thinking about violence, that person is the problem."
Both sides would agree that violent crimes do occur. They might even agree about the quantity. It doesn't matter, though, because neither view is a function of a quantitive perception of the amount of crime. The Texans won't change their view if the amount of crime decreases, and the Europeans won't change theirs if it increases.
I'll give you another example from my personal experience. In the USA, we have two major political parties, the Democrats and the Republicans. I agree with the Democrats on more individual issues, but I nonetheless identify more with the Republican party. This is to say my conceptual view of the world is a better match for the Republicans, who seem to think that people should be responsible for themselves, and that people should get good or bad things in accordance with what they deserve. The democrats, on the other hand, seem to believe in a government whose function is to take care of people, who are often not at fault when they end up doing bad things, but are simply confused; however well-intentioned, I find this paradigm restrictive and stifling.
I could disagree with the Republicans on every single issue and still find that I related to them better, because they would be talking in concepts I understand and use, and the Democrats would be talking in concepts I dislike and find foreign.
I think it is very broadly true that the position people will take on an issue is more a function of how the underlying concepts relate to the rest of their view of the world than it is of any quantitative analysis or cost-benefit estimate. With many issues, what we see as a disagreement about the course of action to take is really a disagreement about the underlying conceptual representation of the situation - once one has chosen a representation of the situation, one of the choices for action follows naturally from it. The arguments, to put it differently, are not really about what to do so much as they are about what is.
This is vital to keep in mind when discussing these issues. Suppose you want to convince someone that plan A is better than plan B. The naive course of action is to use concepts and terminology from your worldview and representation of the situation to explain how plan A is better. This is intuitive, but it is not very effective; you're addressing the wrong problem. You're trying to make the case that given your worldview, plan A is better, but this is both unhelpful and unnecessary; it was never in question! The problem is that the other person does not share your worldview. If you want to persuade the person that plan A is better than plan B, you need to show the other person how to look at the situation using the concepts of worldview A instead of B, and try to convince the person to use this worldview instead. Once that is done, the superiority of plan A will follow trivially.
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