1. Of course extreme situations are what we need to be concerned with. Nuclear weapons, genocides, ecological collapse, epidemics, the theft of billions by business executives, immoral pre-emptive wars, being able to "disappear" your own citizens, being able to lawfully detain a person indefinitely without charge - all very real things, all very extreme, all happening right now. And yet the countries doing this tend to have signed onto the concept of rights, haven't they? Strange how those who embrace human rights are also those who happen to be doing the most damage to them.
2. There is no solution that fits all situations, of course not. Which is why taking a strict-rights approach makes no sense. Ideology is wrong, and doesn't work, and rights-based political philosophy is ideological to it's core.
3. Extreme situations are not rare, and they are becoming more prevalent every day. So yeah. Colour me concerned.
4. You're not illogical. What you say is usually right; why you say it is completely wrong. That makes you better than about 95% of human beings.
5. Government isn't a blind slobbering gun. People are. You are making the same argument towards government than many do towards guns.
6. I'm not going off the deep end, and it saddens me to hear you say that. I am just unwilling to make all sorts of completely illogical mental leaps in order to justify an ideology that wouldn't work, on the basis of a concept that makes no sense (libertarianism and rights).