Both of you are wrong and so is Dustin Kirkland (whoever he is). The core of your error is in this statement:
Only secrets can be used as token for authentication.
That sentence is true, as stated, but only because it includes the word "token". Yes if you're using secret tokens for authentication, then the tokens must be secret. But exchanging secrets (or proof of possession of secrets, which is what most cryptographic authentication protocols do) is not the only way to do authentication. Not by a long shot. In fact, humans hardly ever use secrets for authentication.
How do you identify and authenticate your mom? Do you ask her for a secret password? Of course not. You use the same tools for both identifying and authenticating her, and those tools are a set of biometric markers. The same set of tools are also used in high security situations. Back when I was a security guard in the Air Force, I was trained that personal recognition is the very best form of authentication. Not only is it not necessary to check the badge of an individual you know personally, badge-checking is inferior to personal recognition for authentication (note that badge-checking may still be important for authorization, verifying that the person who has been identified and authenticated actually has permission to enter. Thus I was trained to always check the access control list before allowing someone near nuclear weapons).
With respect to user authentication in electronic contexts we generally use secrets because computers don't (or at least haven't) had the ability to use the sorts of biometric authentication that humans use quite effectively. But, when we equip them with biometric sensors, they can.
HOWEVER, this does not mean that biometrics are useful for authentication in all circumstances.
Secret-based authentication has the advantage that -- assuming the secret has sufficient entropy and can be assumed not to have leaked nor been intercepted and cannot be rerouted (note that that's a pretty long list of criteria, some of which are hard to establish) -- you don't have to worry about the possibility that the authentication could be spoofed. An attacker who doesn't know the secret can't fake knowing the secret.
Biometrics, though, are not secrets. They are public knowledge. This means that an attacker must be expected to have access to copies of our fingerprints or faces. The biometric authentication process is different, though. It does not rely on secrecy of the authenticator, but instead on non-replayability. If we can be certain that (for example) the fingerprint placed on the scanner belongs to the person we wish to authenticate, and that the stored template we match against belongs to the person we wish to authenticate, then we can perform a good authentication. The fact that the fingerprint is not secret does not matter.
Where biometrics fail is if (a) we can't be certain that the livescan data acquired from the sensor belongs to the person trying to authenticate or (b) the stored template belongs to the person we wish to authenticate. Part (a) is particularly difficult to validate in many contexts because faking the input isn't necessarily hard to do, and in some cases an attacker can even bypass the sensor entirely and simply inject a digital copy.
This doesn't mean biometrics are worthless, it just means they're only useful in certain contexts. And, again, their utility for authentication has nothing to do with their secrecy. And rotation is likewise irrelevant and silly to discuss. You need to rotate secrets because you can't be certain they have stayed secret and because if they have low-ish entropy they may have been brute forced. None of that applies to biometrics because they're not secrets and their utility as authenticators does not depend on secrecy.
Can we please kill this incorrect meme about biometrics as identifiers, not authenticators? They can be either, or both, and are used as both, by billions of people, every day, with high effectiveness and reliability. Whether or not they provide security depends on the context.
With respect to credit card payments, fingerprint and facial recognition biometrics are pretty reasonable tools. This is especially true if the sensors are provided by the retailer, and the consumer is providing a traditional electronic authentication (cryptographic challenge-response) with their smartphone or smart card. It's not quite as good if the smartphone is also providing the fingerprint scanner and camera, because in the event of an attempted fraudulent transaction that means the attacker is in control of those components.
But you also have to consider the model that is being replaced. Is fingerprint plus face recognition better than a signature which is theoretically matched by a non-expert human, but in practice never checked at all? Absolutely. Is it better than a four-digit PIN? That's debatable, but it's at least in the same ballpark.