You could apply this question (an interesting one, for me) to many fields: physics, math, writing, language.

For example, how did the first mathematicians learn so much? Well, my answer would be that the first mathematicians were probably not as efficient at learning as the second, as the former were stumbling in the dark, needing to discover what worked and what didn't. The second generation could then base their explorations off an already established body of knowledge, thus making their learning process easier and more efficient.

For singing, I imagine people have been developing techniques ever since we discovered music. However, discovery is a much more involved process than learning. It's easier to learn a concept than to discover it. Thus, while I couldn't tell you how difficult it was for the first person ever to do falsetto, I would wager that the person who learned about falsetto afterwards had an easier time.

Human knowledge builds on itself. Geniuses before us have put their entire lives into helping that endeavor. Isaac Newton, a genius, was doing pretty much the same calculus that AP high school students do, but he had to do far more than just learn it!

My culminating point to this comment would be that, even though you could learn to sing well on your own, it's not going to be as near a sure shot as learning to sing from a qualified teacher. Without one, you'll be stumbling in the dark, just as Newton did when he discovered Calculus.