Another way to think about it: If the voltage-to-current transfer characteristic of whatever you're working with is symmetric about the y axis, then taking the

Another way to think about it: If the voltage-to-current transfer characteristic of whatever you're working with is symmetric about the y axis, then taking the maclaurin series gives you a polynomial with only odd terms. If you apply a sinusoid to that, you get odd multiple harmonics. Working through the same reasoning with an asymmetric transfer characteristic means you get even polynomials as well, which means you get both even and odd harmonics.