Also red meat is a luxury and if you can eat it regularly that means you're doing well economically, that most likely correlates with good healthcare access and a higher level lifestyle, which very much is correlated with better mental health.
This is bit like saying people with expensive cars have less cavities. That doesn't mean driving a luxury car somehow benefits your teeth, its just if you can afford a $100k car, you probably can afford regular checkups and good teeth care.