"Irreversible" feels like an overstatement for a planet that has documented swings in both its temp and atmospheric composition. I'd agree the timescales of changing warming trends is certainly slower than birth rates, though.
Fine, irreversible on a human scale. The last time the earth was this hot (known as the Eemian period) was back when humans just started migrating from northern Africa to the Arabian peninsula, ~125000 years ago.
That's a whole lotta damage done in under 200 years since we industrialized.