There is not any research supporting the idea that you can grow out of OCD. Despite this, many patients resist seeking therapy because they hope their OCD will just pass. When this doesn’t happen (and in many cases, OCD worsens over time), they finally enter therapy.
Once people with OCD are in therapy, however, there is a significant chance for them to see improvements in their symptoms. They can learn how to handle the obsessions and resist doing the rituals, allowing for a life that is not controlled by their OCD. Though people will not grow out of their OCD or be able to ignore it into submission, therapy, medications, or a combination of both can help them learn coping strategies and behavioral changes that can, at least outwardly, seem like a cure.