Another simplistic perspective.
Is a handgun's purpose to kill or not to kill?
If you take firearms training are you learning to kill or not to kill?
Another fuzzy gray-area answer: it depends
In answer to the first question, it's hard to speak of an inanimate object having a "purpose". You can't even really speak about its designer's purpose in creating the firearm, if you're being precise (perhaps it was "to make money" -- a lot of products are designed for exactly that reason). So, maybe the question is, "What is this firearm designed to do?" It depends on the firearm. Some handguns' design is optimized for target shooting, for very precisely being able to punch holes in a paper target, and that's it. Considerations of being able to kill or do damage are absent. But I think it's fair to say that such a firearm represents a departure from the original purpose of firearms, which was to kill, and specifically, to kill people.
The answer to the second question is also "it depends", on the person and the training. I have a good friend who's a firearms instructor, and my impression is that the basic NRA course puts most of its effort into teaching safe operation, i.e., not shooting anything that you don't intend to shoot. Beyond that, you get handgun retention, and beyond that is learning to use the firearm effectively as an offensive weapon. I don't believe there's any training in trying to use a firearm as a deterrent or as a limited weapon (trying to control someone with it vs. using its offensive potential to the max). So that's the general purpose course that is probably the most common in the US -- but again, you've got courses that are focused on hunting and courses that are focused on target shooting. If I were to take firearms training, my most convenient alternative would be the rod and gun club across the river from my house, and they're all about either hunting or pistol target-shooting. It's funny, I'm the only one of my neighbors and one of a minority in town who doesn't own a firearm -- and I doubt one of those people owns a firearm for self-defense.