Suicide/homicide argument

Anti gunners love to break out with the "gun death meme" and claim that 30,000 Americans are killed by guns every year. I point out that the only way that this number is accurate is to include the 22,000 or so suicides each year. I point out that there are only about 8400 firearm related homicides each year, and making guns illegal will not stop someone bent on suicide from kissing a train.

Here is an example of the counter argument that I have been getting from them:

I'm well aware that there's plenty of ways to kill yourself if you had the wherewithal to do so. But I'm also not the one trying to discount deaths in this country vis-a-vis guns. I'm hearing that a lot, now, and I'm declaring that I won't let ya'll have a free pass with death rates by subtracting that number. 

Here is my counter argument to that:

If I don't get to ignore suicide, then you don't get to ignore that murderers and people committing suicide simply choose other tools to accomplish the task, once guns are made illegal. After all, if the goal is to save lives, a person who is strangled to death or leaps from a tall building is just as tragic and senseless as a person who is shot.
So let's count suicide AND homicide rates from all causes, not just from firearms, and see if eliminating firearms actually saves lives..

The US has a combined suicide/homicide rate of 16.6 per 100,000
South Korea, where firearms are virtually illegal, has a rate of 29.8
India, with gun laws FAR more restrictive than the US, 24.6
Japan, where guns are illegal for private ownership sees 18.8 deaths per 100,000 people.
Canada, where there is severe gun control and handguns are virtually illegal: 18.3 per 100,000.


Each of the nations listed above have gun control laws that are FAR more restrictive than the United States, yet people are dying from suicide and homicide at rates significantly higher than the United States. It's almost like firearms have little to do with suicide and homicide, and seems like your argument is not intended to save lives, but is instead a means to your true intent of banning those icky guns, because you don't like them.