Small changes in inputs lead to small changes in ouputs.
This assumes the Earth is a linear system. But it's not. There are many climate-related feedback mechanisms which, once excited, can lead to unstable, out-of-control changes. For example, ice-albedo feedback. A small rise in termperature is not just a small rise in temperature. It can result in reducing the reflectivity of the Earth's surface (the albedo ) by melting ice. This in term increases the absorption of sunlight, which leads to more ice-melt and off we go. It works in the other direction too. Decreasing temperature causes the albedo to increase as ice forms. This can lead to uncontrolled cooling.
It is a respectable, if not uncontroversial, hypothesis in Earth science, that at several points in the past (roughly 750-580 MYA) this uncontrolled cooling led to massive ice formation around the entire planet. This is the snowball Earth hypothesis. Here is a paper by Paul Hoffmann, a major snowball Earth proponent.
These snowball events may have also led to immediate and rapid heating. Can you imaging sea temperatures of 50C at the equator? Or global sea ice thickness of hundreds of meters melting in barely 100 years?
So the next time someone says that a few degrees warming won't be a big deal. Be sceptical and question assumptions of climate linearity.
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