The problem is not that humans eat meat, but the amounts they consume.
Modern humans eat more meat now than ever before, and more beef than ever before compared to other meats - and a lot of that protein is just peed out because the body does not use it.
Even back in the 1980's people (in the West) did not eat as much meat as they do today, and they did not starve. You got a pork chop maybe on Sundays. Steak only on special events. Now it is all beef, beef beef and the fine parts of the calf. Even hamburgers tend to be made from prime cuts these days.
Back in humanity's past, when you got meat, that was a special event - and that is why it tastes so good.
Our teeth, the enzymes in our saliva and the build of our digestive tract were made for a primarily plant-based diet with the occasional meat. Eating too much meat is unhealthy - it increases the risks of many diseases, including cancer.
Even if you are a vegetarian, you don't even need to think much about protein-rich foods unless you are a professional athlete who is out to build muscle. There are small amounts of protein also in bread, corn and most other things you eat.
