Stress from school can absolutely cause mental illness in a student, especially if they are predisposed to mental illness due to other factors. A student who has a genetic predisposition to anxiety or depression may be more affected by certain stressors than one who isn't. Many underlying mental illnesses come to the surface during the teen or young adult years, and exposure to high levels of stress can be the catalyst. Failing a class, struggling with assignments, or conflicts with a teacher or professor can all be sources of stress.
School stress and mental illness can exacerbate each other, as mental illness can negatively impact school performance. When a student isn't performing well at school, they will likely experience even more stress and anxiety. They may find it difficult to concentrate in class, study texts, or do well on tests or assignments, and may not even feel motivated to attend class or participate. This can be a difficult-to-break cycle that can lead to burnout or more severe health issues.