Its only taken other forms...
"We stopped natural selection as soon as we started being able to rear 95-99 per cent of our babies that are born. We are the only species to have put a halt to natural selection – of its own free will, as it were."
But natural selection doesn't merely stop at birth. How many of those babies who got born mainly thanks to modern medical science have actually managed to live up to a commonly normal age? Not many.
Which is another aspect of natural selection; weeding out the weak. And although I most certainly agree that this process seems to have been slowed down, I don't think we stopped it. Not by far; one can't ignore that people continue to die long before their full lifespan.
Now, this may not be a very popular comment to make, I don't mean any disrespect to the families who may have had to suffer from situations like these, but what about people who manage to kill themselves in traffic, for example through use of excessive speed, crossing the railway when "nothing is coming", or other means? I think there's much more to this issue than merely looking at babies. Because if we have evolved, then why couldn't the process of natural selection have evolved with us by taking other forms which are just as ruthless?
And that's not even taking a more common aspect such as natural disasters into account.
Which is another eery thing to consider: what if we only have managed to stall things? Meaning; for all we know a disaster could happen tomorrow claiming a huge number of lives. Freak accident? Natural disaster? Or a new form of natural selection?
I don't think one can really make claims such as these. We didn't stop anything in my opinion.