We are already in the middle of a mass extinction caused by human activity. Even in the wikipedia article you linked it talks about extinctions of 40% of species if we get to 3 degrees of warming.
There is high variance in estimates about loss of biodiversity, but if you start looking at what happens to plants and animals with climate shifts there is a tremendous and almost unfathomable risk there. Many species depend on certain temperature ranges for key parts of their life cycle. Fruits don't develop in the temperature is too hot or too cold. Many animals that depend on that fruit, end up starving if those fruits don't develop. Then there's the fact that any organism can only take but so much heat. In heatwaves there's a temperature beyond which is lethal for many organisms. And if heatwaves arrive during breeding season, the young of many animals will be particularly hard hit.
When you get to the oceans, increased acidity due to carbon absorption will lead to fisheries collapse and the extinction of corals. Ocean acidification will prevent many forms of plankton from forming their shells, which undercuts many open ocean ecocystems. Something like a billion people depend on fish as their primary protein source.
As for humanity, people are really focused on where climate will be in 2100. But what happens in 2200, 2300, 2400 and on if we don't get things under control? CO2 can stay in the atmosphere for thousands of years. So if humanity doesn't curtail emissions and temperatures rise by 3 or 4 degrees, it's going to stay at least that hot for millenia. But even worse, all the methane that will get released by thawing permaforst will accelerate warming even beyond that. Melted glaciers and sea ice means less sunlight will be reflected back into space, which will cause even more warming.
There is high variance in estimates about loss of biodiversity, but if you start looking at what happens to plants and animals with climate shifts there is a tremendous and almost unfathomable risk there. Many species depend on certain temperature ranges for key parts of their life cycle. Fruits don't develop in the temperature is too hot or too cold. Many animals that depend on that fruit, end up starving if those fruits don't develop. Then there's the fact that any organism can only take but so much heat. In heatwaves there's a temperature beyond which is lethal for many organisms. And if heatwaves arrive during breeding season, the young of many animals will be particularly hard hit.
When you get to the oceans, increased acidity due to carbon absorption will lead to fisheries collapse and the extinction of corals. Ocean acidification will prevent many forms of plankton from forming their shells, which undercuts many open ocean ecocystems. Something like a billion people depend on fish as their primary protein source.
As for humanity, people are really focused on where climate will be in 2100. But what happens in 2200, 2300, 2400 and on if we don't get things under control? CO2 can stay in the atmosphere for thousands of years. So if humanity doesn't curtail emissions and temperatures rise by 3 or 4 degrees, it's going to stay at least that hot for millenia. But even worse, all the methane that will get released by thawing permaforst will accelerate warming even beyond that. Melted glaciers and sea ice means less sunlight will be reflected back into space, which will cause even more warming.