Confused about some μεν... δε constructions.

I am working through the ΛΟΓΟΣ textbook. This contruction has me scratching my head (p. 44 if you have the book). I’m sure I am missing something obvious.

Ἀνθρωπόμορφα ζῷά ἐστι καὶ ὁ μινώταθρος Ἀστερίων, τὸ μὲν ἥμισυ ἄνθρωπος, τὸ δ’ ἥμισυ ταῦρος…

I can translate it fine, but it isn’t immediately obvious to me why “τὸ μὲν ἥμισυ” and “τὸ δ’ ἥμισυ” should be neuter.

ἥμισυ ”a half” is neuter, regardless of the gender of the thing it is a half of.

”(The one) half human, (the other) half bull”

Thanks so much! ἥμισυ has masculine and feminine forms. Why is it always neuter in this context? I ask not so much for the sake of understanding this sentence, but because I think I’m missing a larger gramatical puzzle peice.

When used as adjective, it takes the gender and the number of the noun it qualifies – ἥμισυς λόγος, ἡμίσεες λαοί etc., you can find examples in LSJ.

Here however we have the noun τὸ ἥμισυ derived from the adjective. These are typically neuter.