I’ve got four degrees - no-one ever suggested I head to trade any of them in. Sounds weird to me.
I have a BA in Philosophy (UC Davis 1980) and a BA in Business Management (Cal State 1986) and never heard of relinquishing one degree for another. On the other hand, I have met career counselors who are idiots; when I was in school I learned quickly never to rely on them for accurate information. What teed me off is that they are paid so much and know so little.
The issue might not be “relinquishing” so much as “desist from representing.” I completed an MA in Creative Writing and then became a psychologist. My professional ethics, and the law in my state, specify that when I describe or advertise my professional services as a psychologist, I can only name my degrees in my professional field. This is intended to decrease confusion about my qualifications. It may be that the BFA can’t appear on the business card or any other professional announcements because it’s not related to the training/licensing received in the professional field being advertised, and would confuse the public (at best) or defraud it (at worst).