>You can't recycle to infinity.

The lifespan of the earth is not infinite, pretending it is is foolish. We have about 5 billion years on earth before it will be consumed by the sun. Presuming an infinite earth creates a very obvious, simple, and wrong conclusion about something that is actually very difficult problem.

>The logical conclusion is that at some point we run out of resources.

The point of renewable resources -- like solar -- is exactly that they are renewable or effectively infinite.