Worst-case projections show that at our present CO2 growth rate, things will get bad rather quickly, but keep in mind that the Earth's climate cycles have many (not well understood) self-regulation systems. Increased atmospheric CO2 may lead to explosive vegetation growth which may lead to increased carbon sequestration.
An extremely well-understood effect is that ocean acidification thins the shells of shellfish.
This may seem like a minor effect, but rapidly upsetting the food chain of the ocean seems like an absurdly risky experiment to run on the planet we inhabit.
And back when CO2 levels were higher, how many humans were around? Fortunately none.
Nobody claims it will end life on earth. It might just end life as we know it as a species given we never hunted dinosaurs.
> Increased atmospheric CO2 may lead to explosive vegetation growth which may lead to increased carbon sequestration.
To my understanding this is decently modelled in long term climate simulations. Plants won't save us and the increased absorption rate of plants with higher CO2 levels is well studied in the lab and accounted for.