This is to specifically address class struggle as it relates to the ecological crisis. It will not address all the other (many!) reasons that working class struggle must be waged and supported.
First, we must recognize the fact that global capitalism is driving ecocide.
The problem reaches much farther back than capitalism itself. The combination of an early gendered division of labor with the adoption of agriculture and corresponding formation of permanent settlements set the stage for class divisions and the private accumulation of surplus wealth. Maintaining this arrangement required the development of states with armies, social oppression and repression to weaken internal opposition, and ideologies to make it all seem normal and pre-ordained. And as land was degraded and resources used up faster than they naturally replenished themselves, expansion became imperative, leading to conquest and forced unequal trade. These intertwined and matured over time into an ever-more complex tangle, culminating in late-stage capitalism: the all-encompassing, all-devouring, spectacular horror that is our current global social living arrangement.
The environmental crisis, specifically climate change, is the most urgent problem we collectively face. It is a simple fact that if our planet no longer supports life, then all human pursuits, including social justice, will also come to a screaming halt.