But now you’re cherry picking food. Fish and chicken is good and healthy food, why didn’t mention those instead. Pure sugar is both vegan and gluten free, but you wouldn’t call that healthy would you?

There is nothing unhealthy about gluten if your body can tolerate it. So vegan, gluten free and the opposite are all perfectly valid options for a healthy diet. You could also have an unhealthy diet within those 3 categories as well.