I don't know where you got that idea, but we're not even the most populous species of vertebrates on the planet (that might be chickens).

If you include arthropods, ants make it not even remotely close.

If the trend doesn't reverse, it's mathematically guaranteed.

But realistically, I agree. Civilizational collapse would happen long before extinction, which seems like it would almost certainly return the birth rate back to pre-industrial levels. I just don't think that's a desirable outcome either.

Or, even more realistically, nations with state religions that effectively outlaw birth control and/or women's rights will take over the world, and nations which don't do those things will collapse. That also seems like a bad outcome to me.

Point is, I don't think it's wise to treat this like it's not a problem.

https://en.wikipedia.org/wiki/Passenger_pigeon

> The pigeon migrated in enormous flocks, constantly searching for food, shelter, and breeding grounds, and was once the most abundant bird in North America, numbering around 3 billion, and possibly up to 5 billion.

Past performance is not indicative of future results.