What's so special about octaves?

Really a question about tonal perception:
Even someone without musical training will recognize some kinship between two notes an octave apart. They’re not the same pitch, obviously, but they are, in some intuitive sense, “the same note”. Our conventions for naming notes recognizes this, but I don’t think our perception of this “same note but different pitch” derives from our notation conventions.

So I can’t help wondering why this octave interval should be so easily and naturally recognizable to our ear. Why could most 10 year-olds effortlessly sing an octave interval, but not a fifth or third? After all, we hear fifths and thirds as much as we hear octaves in Western music.

Hope this makes sense