While capitalism is a big accelerator of climate change, socialism could do the same
The difference is that capitalism by its nature requires the degradation of the environment. Capitalism, by definition, needs to increase profits year after year. Unlimited growth is impossible in a finite planet with limited technology without degrading the environment, so capitalism simply ignores the climate in its quest for higher profits. After all, you can’t risk getting outcompeted by another company which will be less afraid of abusing nature.
Socialism, on the other hand, doesn’t need perpetual growth. The objective isn’t infinite profit, the objective is higher living quality for people, which doesn’t necessarily rely on increased material wealth, especially not in a context of degrading climate which negatively affects the quality of life of people. It doesn’t mean socialism doesn’t have to work hard to prevent degrading nature, it just means that it’s not a necessary logical consequence of socialism whereas it is of capitalism.
You talk about historical proof. The reality is that historically, the groups concerned by climate change have consistently been to the left of the political spectrum, whereas the right wing (capitalism’s most loyal defenders) doesn’t seem to care. For 36 years we’ve had an International Panel on Climate Change (though ExxonMobil had reports of Climate Change being manmade since the early 70s and hid them), and for 36 years scientists have been saying the same: we’re not doing enough. What’s been the response of capitalist governments everywhere? “We shall continue not doing enough”. How many years of capitalism in all countries failing to step up to the problem do you need to realize that capitalism simply has no incentives to solve this problem because it’s fundamentally an antidemocratic system, in which the interests of a few in the owning class are held above those of the working class?