Our society is much more complex than our biology expects.

Also, clearly you have never lived in the Midwest. Even in some parts of modern day society 14 year old boys are adequate hunters :).

Teenagers having babies is not the solution to birth rates.

Agreed, but I would go further and say falling birth rates aren't a problem at all (unless you can think of something that requires more than 6 billion people to accomplish).

But we don't produce more than we consume of some resources that seem important to our modern way of life (water, oil, etc). And off the top of my head I can't think of any good reason why having more people would bring us closer to making things like fusion a reality (other than by increasing the need).

Basically, there are no particular shortages of anything that will necessarily be critical; the main thing we need to do to get over the hill we can see coming up is to stop braking so hard on the downslope of this hill. :)

People consume resources that are largely non-replenishable, or at least are not replenished in a manner strictly related to the number of people. As abstractbill says, people don't produce water. Similarly, more people doesn't typically mean more food either, although it might indirectly through the increased needs of more people leading to more farmers etc.

What people "produce" is generally 'order' or increased labour output. Whether this leads to supporting more people I'm not sure.

People can easily produce water in the same sense that they "consume" water (since consumption in this case merely means to pollute a little bit, and cleaning water only requires energy and physical plant).

If you use prices as a proxy for measurements of how much we have available, it's clear that the vast majority of the resources we use are, in practical terms, more plentiful now than a century ago, and given that we can see how to switch to more plentiful resources still, I don't see that trend stopping for at least a century or two, at current rates. Even if our technology didn't improve fundamentally past what we know how to do now, we'd have at least a century before we had to go get more resources elsewhere, and we already know how to do that (though we'll need a lot more engineering to actually do it, of course). Meanwhile, the more people there are, the more engineers and innovators there are. If we don't get hit by an asteroid or literally destroy ourselves, the future is pretty damn bright. :)

Whenever you see someone writing sweeping generalizations about rural or suburban life, you can bet that person is parroting things they heard or assume to be true from their wonderfully urbane life.

But even better, when I had the opportunity to move to big cities, they were even more fantastic and exciting because I was from suburbs. I can't imagine growing up in a city and getting bored with it, before I'm even old enough to take full advantage of life there!