Or maybe it's a habit. What's the purpose of running red lights? Or of dinosaurs? Nothing so far you mentioned proves the "intrinsic value" of anything except what we personally or as a society make up. I love that program "Life after People" that shows how the world and even our pets would do just fine if suddenly the humans were to disappear.
The world existed before us and could continue existing after us just fine. The entire human history is a series of scenarios with faceless players trying to make this world, indeed all of existence, about us.
On a tiny spec of dust in space, a blue dot no one is near enough to even notice, about as notorious as an ant that was hatched last week in my back yard.
Purpose and "intrinsic values" are feel-good constructs.
What possible purpose could you have for saying that?
And, I guess, the world would go on if our pets were to disappear, or our loved ones were to disappear. That doesn't make either a good thing.
I really don't get the anti-your-own-species view. Certainly there are evil human beings. There are also good ones. Those that, in the extreme, see our species as loathsome are, IMHO, expressing a slightly broader view of their own self-loathing.