Why does this not make sense? Please explain.

Because of the central limit theorem, many distributions encountered in science are approximately Gaussian, which is parameterized by its mean and standard deviation. According to Wikipedia: "Height is sexually dimorphic and statistically it is more or less normally distributed, but with heavy tails."

On top of that, we have well-understood and easy to compute estimators for standard deviation. Using the sample variance is not a bad estimator at all, the only real disagreement is whether you divide by N or N-1.

It makes no sense in that it has no physical meaning. As you say, even without deeper meaning it is a fine tool for handling Gaussian distributions.

Indeed, why does it not make sense? I read that, I immediately know that about 68% will be between 165 and 170 cm. http://en.wikipedia.org/wiki/68–95–99.7_rule

That rule only applies to normal distribution. So you would have made an assumption.