I was managing projects for years before I knew there was something called "project management" as a formal discipline or knew anything about the PMI, IPMA, or other project management organizations.
For those of us who view ourselves as "Project Managers" or have that in our title, there are many, many more people who are managing projects in some capacity who don't.
Just as with any other skill, if you focus on it as an area of study and as a formal discipline, you WILL get better at it. Project management is a skill set in use by just about everyone, every day. As far as I'm concerned, it should be a standard part of the public education standards for high school, because everyone can benefit from some basic project management know-how.