The short(-ish) version? "Bone-conducted sound," which is essentially an excess of vibrations from both inside and outside the body that makes your voice sounds deeper within your own head.
You're used to this sound because of the "mere-exposure effect," which means we favor things that we're familiar with. When we hear our voices played on a recording, those vibrations are obviously not included, leading us to hear the actual sound of our own voices, which we hear way less often.
It's simple, really: we fear what we do not understand. Just like all those apes in Planet of the Apes.
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Jeremy Glass is a writer for Thrillist and thinks his voice sounds weird pretty much 100% of the time.