Well, a meat exclusive diet would be deficient in things like vitamins C, K, & E, likely Calcium, likely Magnesium (unless you're really chowing down on bone). As well as denying any beneficial phytochemicals present in plants. You'd also probably end up with too much zinc, copper, iron, etc...

And it's not as if our bodies aren't capable of dealing with moderate amounts of oxalates, phytates, lectins, goitrogens, etc...