Left-handedness is linked to a risk of mental health issues
Left-handedness is linked to dyslexia, some mood disorders, and schizophrenia. Research has also shown that people with schizophrenia are more likely to be left-handed than those with bipolar syndrome or depression. The study, "Left-Handedness Among a Community Sample of Psychiatric Outpatients Suffering From Mood and Psychotic Disorders", showed an 11% prevalence of left-handedness in mood disorders, which is similar to the rate of the general human population.
Many researchers and psychologists agree that handedness is connected with brain lateralization, which refers to the separated brain--the fact that the two halves aren't exactly the same. You may have heard of this being split up as the right brain and left brain, with left-handed people primarily using the right half, and vice versa. However, it's not as simple or as black-and-white as that. Many left-handers also heavily utilize leftmost areas of the brain more so than the right. Scientists are still trying to really nail down the correlation with handedness and brain lateralization.