Was climate change inevitable anyway, or is there more to it?
Earth's climate has changed in the past and will change in the future. It would have changed even if we didn't start spewing enormous amounts of CO2 to the atmosphere. The main difference here is the rate at which this is happening. Natural climate change unfolds over thousands or tens of thousands of years (btw - PETM was fairly rapid, but we don't know exactly how rapid). Current climate change happens much faster. You can see temperature records broken every single year.

Our modern civilisation developed in a fairly stable climate. We did not develop in a climate where we had ice-free poles, or higher sea levels. The geopolitical consequences of altering that too fast would be simply too much.