take one's half out of the middle

The story

Referring to a scenario where one is entitled to half of something (e.g. half a cheese-wheel, half a cake, half a bed, or half of the width of a road for driving) but one takes one's half from the middle instead of one side, leaving the other person with a less desirable half (of the cheese-wheel or cake) consisting of crust or rind, or an unusable "half" (of the bed or road) made up of two separate pieces on either side.