You can still eat animal products and be okay. What's the problem?
The point isn't that carnism is incompatible with healthfulness. Technically, you could eat a 99% vegan diet and (correctly) claim that your "omnivorous diet" is as healthy as a 100% vegan diet, or you could eat a completely plant-based diet and torture animals in your basement. In both of these scenarios, you would be essentially just as healthy as any other vegan.
The point is that eating meat is unethical. Therefore, you would need to demonstrate that it is necessary to avoid some other larger harm to well-being. We almost implicitly accept this for species that we like, such as dolphins or dogs. If you saw someone stabbing a baby dolphin to death in the shallows of the ocean, it would have to be in some (admittedly bizarre) scenario where it was absolutely necessary to stop some other thing from happening. We wouldn't accept the answer that "No it's cool; I'm good and healthy regardless of whether or not I stabbed a dolphin to death or not, so it's all good. Stabbing the dolphin didn't have any negative impact on me". So why then should we accept this answer that stabbing a baby calf in the neck?
"I can drive around in a stolen car as well as I can in one that I legally purchased". That wouldn't seem to be a compelling defense for stealing cars. Similarly, it's not a defense for the unethical actions of eating meat.
Any vegan that is attempting to demonstrate that veganism is healthier than meat-at-every-meal carnism is arguing for more than they need to. It's incumbent upon the carnist to show that eating meat was necessary for some reason.