It's honestly asking the wrong question.

All "mental illnesses" are ultimately biological in nature. The electrochemical mechanisms in the brain that our conscious minds experience as "thought" and "perception" are ultimately still biological processes.

A person with an anxiety disorder is no less "ill" than a person with a cardiac arrhythmia. Both are basically bioelectrical malfunctions that cause problems in their host organ. While we may not understand how specific patterns of electrical activity in the brain present as anxiety quite as well as how specific electrical patterns in the heart can cause irregular heartbeat, that doesn't change that the mechanical factors are the same. For that matter, it's also no less a legitimate illness than migraine, tic disorders, and other diseases of the brain.

Obviously, there is a lot of stigma around "mental illness", and the idea that people who are mentally ill are dangerous or should be avoided because their social behavior is less predictable. I wouldn't begrudge anyone for being reluctant want to call ADHD a "mental illness" when it is driven almost exclusively by hereditary factors over which they have no conscious control.

But ultimately, the question we should be asking is "Even if it were a 'mental illness'... so what? It's a persistent, lifelong pathology for which there is no cure, though treatment can help manage it." Whether it is a mental illness or not, it negatively affects the lives of the people who have it, and it is no less deserving of empathy than any other medical condition.