Let me illustrate. The murder rate in Washington, DC is pretty high, at 13.9 per 100,000 (which I'll abbreviate as just 13.9 from here).

I live in the DC area. Does that mean that I live in an area with an extremely high murder rate? Nope. I live in Fairfax County, about 15 miles from downtown, but still well within the urban area. At first glance, Fairfax County is a collection of suburbs. However, this is kind of misleading, as the county has almost double the population of DC proper, about 1.1 million people. In 2011 (the most recent year I could find a figure for), there were 11 murders in Fairfax County, putting the murder rate at just under 1.0. That makes Fairfax County on par with or safer, on average, than every Australian state besides Tasmania.

And this isn't cherry-picked, aside from the obvious bit where I started out with it because I live here. neighboring Arlington County, for example, with a population of about 220,000, had no murders in 2011. Montgomery County had 16 murders in 2011 out of a population of about one million, for a somewhat higher murder rate of 1.6.

There is substantial variation within each jurisdiction as well. Large parts of DC is perfectly safe, with murders concentrated in certain areas:

http://apps.washingtonpost.com/investigative/homicides/

If you live in the northwest part of the city, you're perfectly safe. If you live in southeast, life is even more dangerous than the 13.9 average rate suggests.

DC is a somewhat special case, as a large urban area carved up into many jurisdictions. Other major US cities tend to have fewer local jurisdictions, which makes it harder to see the individual regions. Chicago, for example, has a population of 2.7 million within the city limits and that encompasses a huge range in terms of crime, from places where you'd never want to get out of your car to places that haven't seen a murder in years.

Yes, the US has more violent crime than other first-world countries, but it doesn't much apply to the average person. Much of this crime is criminal-on-criminal violence, and much of the rest is concentrated in poor and minority areas. That's not to excuse it at all, or to somehow imply that it makes it OK, but it is relevant when addressing what most of the country sees.

The rest of the world works exactly the same way too.

Yes, there are places in the us that have little violent crime. There are more places like that outside the US though, and taking population into account my point stands.

But the fact remains that most of the US does not suffer from extreme violence, and comparing the averages across countries doesn't do anything to dispute that.

Even though you claim to understand this, you didn't let it stop you from declaring that "most of the US does have a higher murder rate." How does that work, then?

In areas of similar population density, the murder rate in the US is higher.

Of course there are areas of the US that have very low population density, and an equally low murder rate.

I really can't keep track of just what you're actually arguing, nor do I care to keep trying.