How do we know that most of the species that ever lived are extinct?

It's been a long time since I've responded to an Uncommon Descent post, and I'm starting to remember why. There's one that went up over there the other day on the fossil record that's really almost mind numbing - starting with the title, which is "[Why Not Accept the Fossil Record at Face Value Instead of Imposing a Theory on it?]("

Here's what seems to be the main argument:

Here’s a simple example - extinction estimates. Darwinists will say that 99.99% of species that have ever lived have gone extinct. Well, that’s actually a bunch of B.S. There are roughly 250,000 species that have been identified in the fossil record, and well over 1,000,000 species that exist today. Taken at face value, even if every species in the fossil record has gone extinct (which they haven’t), that means that 80% of species that ever existed ARE STILL ALIVE. That’s quite a stretch. So where do Darwinists get their number? By assuming that innumerable species existed in the transitional spaces. Why? Because they must have existed there for their theory to be true.