As for the bit that confused you, perhaps that wasn't the best way to put it. The -3dB point is the conventional place to define the "start" of the pass-band. In this sense, it is an assumption, of where we conventionally draw the line.
But the bit about the impedances being equivalent (by which I meant, have the same magnitude, but different phase), is not an assumption. It's simply that the output falls off to one-half the power at the point where the impedances are equivalent.

I should have thought of Wikipedia, and it's propensity for useful pictures: Corner frequency

As for what EEs do, yes, that's more or less it. You can go into power, where you get to spend your life bored to death specing overhead transmission lines and the like, or you can go to typical electronics stuff (most EEs), which consists of designing all manner of circuits. Or, you could go to various minor specialties, like IC design and such. Wikipedia is helpful again.
CpEs are really more like EEs who know how to program better. (And, on the flip side, aren't as good with heavy-duty analog stuff, like super-heterodyne radios.) But both EEs and CpEs have basic skills in analog and digital electronics.
I have more of a CpE bent, but took the EE course due to difficulties scheduling some of the CpE classes. Sometimes CpE is considered a specialty within the EE field, sometimes as a separate, though closely related, field.

Well, I expect the design specs weren't for "high-pitched, nearly inaudible sound", but rather for ultrasound, i.e. high-pitched, totally inaudible sound. But kids tend to have higher range of hearing, so you could hear it anyway.
I have even heard of some cell-phone ringtones at the top end of human hearing, where most schoolkids can hear them, but their teachers can't!