Claiming that something is on its whole sustainable is rather loosely defined (i.e what level of impact is considered sustainable and on what metrics), so let's look a little closer. What many are saying there is that process is still going to inherently be much more inefficient compared to growing plants directly for human consumption

It turns out to be the case that the worst-case production of any plants-based production comes out ahead compared to best-case production of meat, dairy, etc. on virtually all environmental metrics

If I source my beef or lamb from low-impact producers, could they have a lower footprint than plant-based alternatives? The evidence suggests, no: plant-based foods emit fewer greenhouse gases than meat and dairy, regardless of how they are produced.

[…]

Plant-based protein sources – tofu, beans, peas and nuts – have the lowest carbon footprint. This is certainly true when you compare average emissions. But it’s still true when you compare the extremes: there’s not much overlap in emissions between the worst producers of plant proteins, and the best producers of meat and dairy.

https://ourworldindata.org/less-meat-or-sustainable-meat

Plant-based foods have a significantly smaller footprint on the environment than animal-based foods. Even the least sustainable vegetables and cereals cause less environmental harm than the lowest impact meat and dairy products [9].

https://www.mdpi.com/2072-6643/14/8/1614/htm

Even true of synthetic fertilizer usage compared to the best case of animal manure

Thus, shifting from animal to plant sources of protein can substantially reduce fertilizer requirements, even with maximal use of animal manure

https://www.sciencedirect.com/science/article/abs/pii/S0921344922006528

In terms of biodiversity

Livestock farmers often claim that their grazing systems “mimic nature”. If so, the mimicry is a crude caricature. A review of evidence from over 100 studies found that when livestock are removed from the land, the abundance and diversity of almost all groups of wild animals increases

https://www.theguardian.com/environment/2022/aug/16/most-damaging-farm-products-organic-pasture-fed-beef-lamb

If we compare more typical production rather than best to worst, the differences are even more apparent

To produce 1 kg of protein from kidney beans required approximately eighteen times less land, ten times less water, nine times less fuel, twelve times less fertilizer and ten times less pesticide in comparison to producing 1 kg of protein from beef

https://pubmed.ncbi.nlm.nih.gov/25374332/