To understand this, we need to talk about carbon cycles. I'm going to oversimplify things but you can google it if you want more info.
The short term carbon cycle contains all living things. Trees, plankton, humans, fish, bacteria, insects etc. Carbon gets absorbed from the atmosphere by plants, then re-emitted into the air when things get eaten. The same carbon goes round and round the system. If you cut down trees and replace them with factory farmed cows, you get really bad things like pollution of rivers, global warming because cows excrete carbon in the form of methane. However you can fix it by killing the cows and planting trees again. Methane only lasts ~20 years in the atmosphere, and all the carbon emitted from felling trees gets re-absorbed by growing new ones. There are many travesties like palm oil or bottom trawling. However the overall amount of carbon in the biosphere stays roughly constant. Extinct species are lost for ever, but most of the damage is potentially fixable in a lifetime. Visit the Swaledale in UK for an example of how a polluted 19th century lead mine is now an area of outstanding natural beauty.
The long term carbon cycle is where over geological ages vast amounts of dead animals and plants get buried under layers of sediment. The carbon stays there for hundreds of millions of years in the form of coal or oil. It comes out naturally by erosion, erupting volcanoes etc, but it is an extremely slow process. Unfortunately this fossil carbon is being extracted and burned at a staggering rate by our civilisation. Megatonnes of carbon that should be safely several miles underground is in the air around us, it gets worse every day, and there is currently NO WAY of putting enough of it back underground to make a difference.
Vegans are worrying about the biosphere, which is a very serious, but mostly fixable problem.
However, every litre of fuel we burn contributes to a problem which could be with us for a million years, and we have no solution whatsoever.
IMHO, going vegan is a moral decision about animal cruelty. If like most people you are happy to eat meat, many sources of food cause terrible damage to our ecosystem; need to be boycotted.
However, from a long term climate change point of view, veganism is a distraction from the far far more serious and nigh on irreversible problem of increasing atmospheric CO2 from fossil fuel burning.