Yes. There are specific nutrients that humans can't synthesize and have absolutely zero plant sources. The obvious one is animal protein, which is structured and metabolized differently than plant protein. But more specifically:
- Vitamin B12, you don't need a lot of it (a few grams of meat per week provides more than 100% of the dietary sources), but every single study of populations of Vegans shows that the majority of them are deficient and have Hyperhomocysteinemia as a result. Hyperhomocysteinemia is only ever seen in four populations, the extreme elderly (due to age related nutrition absorption and metabolic issues), third world countries with chronic poverty, extreme alcoholics and vegans. You can get by for a very long time as B12 deficient, but it will catch up to you and the result isn't particularly pleasant. https://news.ycombinator.com/item?id=6883090 some more I've compiled on this
- DHA (Docosahexaenoic Acid), an Omega-3, pretty much available only from animal sources (and a very small algae source which is often used as a supplement precursor) has been shown important to normal cognitive functioning. Every study I'm aware of has shown that vegans are deficient in DHA (even though it can be synthesized from ALA which is the kind of Omega-3 found in flax seeds and chia etc. it's preferentially synthesized to EPA another Omega-3 which also has plant sources). Omega-3 is essential and not all O3FAs are equal. Despite being able to find DHA in algae in sea vegetables, most vegans simply don't eat enough of it.
- Vitamin A - readily discussed in Vegan sources as "available in plants, but hard to get sufficient quantities of a complete source". Vitamin A is a group of compounds, not just one, and plant sources don't offer a complete source. It's readily available in animal sources, especially liver. Vegans are typically deficient in retinol which is used in the development of epithelial cells an essential and basic component of animal tissue.
Non-essential, but had to very hard to impossible to get in plant form in sufficient quantities (i.e. studies of vegan populations show shortfalls in the majority of the studied population):
- Arginine (partially synthesized by humans, but needs to be supplemented by food sources. Animal sources are much better sources than plans. But if you eat sufficient plant sources, which majority populations of vegans have been shown not to do, you can get by.
- Creatine, synthesized by Arginine, along with Methionine (which is better sourced from eggs then plants as well) and glycine (which is readily synthesized by humans), has been shown to be majority population deficient in every study of vegans I'm aware of. Creatine is important for muscle development and maintenance. You'll find that vegan athletes are aware of this dietary shortfall and supplement.
- Carnosine, only available in animal sources. Carnosine has been shown to be an important dipeptide and important in normal muscle function (where it can be used to significantly boost performance with sources of beta-Alanine). It also has been shown to be a major preventative factor in Alzheimers, Diabetes proper skin function and various age related illnesses suggesting long term consumption is important for healthy long-term living.
- Vitamin-D - especially in northern latitudes or people who don't get enough sun exposure. The primary dietary sources are all animal sources (beef liver, eggs, cheese, fish, etc.). Vegans have shown to have higher rates of vitamin D deficiency than other populations.
and it goes on and on and on.
Vegan diets also make adequate nutrition decisions and monitoring more complicated. For example, complete Zinc intake should be at around 15mg per day, but diets high in phytates require more as phytates disrupt zinc absorption. Similarly iron intake has to be measured at higher doses as what humans actually need is Heme, which is synthesized from Iron. Heme only has animal sources, which is generally used to explain anemia that's common vegan populations.
In addition, animal sources are simply required for normal child development even if adults can get by for longer periods without some of the above. Studies of children raised on vegan diets show significant health and cognitive deficits as animal sources are either the only or the best sources of critical bone, blood, muscle and brain development.
Long term studies of vegans have shown that over 90% of vegans are deficient in one or more of the above, despite supplements being a traditional part of the vegan diet. Most vegans do not stay vegans for more than a few years as the health and nutrition deficits build up, they'll wax on and off the diet -- this provides essential B12 at interval, and since B12 doesn't require constant intake, is usually enough to keep off the worst effects of B12 deficiency. Carnosine however has been shown to be a significant problem in long-term vegan (and vegetarian) diets and is generally attributed to the reason why vegans, despite being healthier in several categories, die at ages and rates similar to omnivores.
Every single one of these deficiencies and health issues are solved on normal omnivorous diets.