Drawing is about learning to "see." If you are a lifelong learner and have are continually curious and willing to put the time and effort into it, you'll discover that you have the ability to improve your skills.
I think the fallacy is that often people think that skills such as art and music solely rely on inborn ability, when in fact often those who are best at it, have been schooled and trained in it all their lives. Of course there are the few that are exceptional in these fields, just as there are prodigy mathematicians and sports athletes. But, the vast majority of people who excel at art are those who put the time and effort into it, as well as being guided by someone who already knew how to do it.
If you have the desire and time to devote to increasing your drawing abilities, you will be able to do it.