While I am extremely skeptical of the healthy-ness of a diet entirely made of meat and other animal products, I'm not sure what particular nutrients you are thinking of. The only thing that animal products don't contain that can be found in plants is dietary fiber, and it's somewhat debatable whether to call that a nutrient. But otherwise, meat and other animal products contain all of the necessary proteins, fats, and vitamins. After all, we all live entirely on animal products for ~1 year of our lives, when we exclusively drink milk.

The problem with meat is that it doesn't contain carbohydrates, which are a cheap source of energy, so the body has to work a lot more to get its energy, and with a lot more by-products. Also, the lack of fiber will significantly alter the gut microbiome, and almost always leads to stool issues.