In the lesson you state:
Ni l'un(e) ni l'autre ne... means neither one nor the other or neither (of them).English is my native language and I would never say "neither one nor the other". I would say "Neither the one nor the other" or better, as offered "Neither." "Neither one nor the other" just doesn't sound right. "Neither one" seems sufficient (and a third alternative) making the addition of "nor the other" seem superfluous and inappropriate. I wonder if this isn't a dialectical difference within North America.