This is just simply nonsense. A far -better- argument would be essentially Steve Job's take on death. Which was "I think death is the most wonderful invention of life. It purges the system of these old models that are obsolete....Without death, there would be very little progress." Your argument has been disproven countless times, and will continue to be.
Your head is full of nonsense. Something like 85% of animal and plant diversity on Earth has disappeared in the last 50 years. According to a study by the World Wildlife Fund, more than a third of Earth's natural resources have been destroyed by humans in just thirty years. And yet deforestation has increased to an alarming rate. Have you heard of Climate Change? Guess what's causing that? It is estimated that humans use 173% of the earth's resources every year. You mind explaining how that is sustainable? We're pretty much screwed, and the last thing we need is more people.
Biocapacity can be increased with technology and sustainable energy. Our impact on environment can be eliminated with technology and sustainable energy. These are not a problem at all; we just need to utilize more energy.
Assuming humans never destroy literally all multi celled organisms on Earth, I think this rediversification is guaranteed to happen after some amount of time.
Is the number of species really important at all, or is the preservation of the basic genetic drive the important thing?
There is a race between humans destroying their own capacity to destroy and humans destroying all life on Earth. I would bet on the former.
The parent says, "There's too many people on earth already", you reply "Steve Jobs said Death is great and necessary", these seem like sympathetic points to points.