There's maybe a more direct way of saying that:

"Hey khazhoux, maybe you /are/ sexist for thinking that a vocal trait sometimes associated with young women is a sign of amateurism."

The tricky thing about unconscious bias is of course that it's hard to know when you're carrying it. Nonetheless, I'm fairly confident that that speaking style would be considered un-authoritative by most people, and as a manager I see my job as how to help the individual whose career could be impacted by cultural norms both fair and unfair.