A hill is a highly defensible position. In Ye Olden Dayes, it was very common to build one’s fort or city on top of a hill. The hill would be the last point of retreat, the position from which you would fight to the death.
If someone says, “that’s a weird hill to die on,” or “that’s a bad hill to die on,” it means the subject has chosen a position that is not worth defending. It implies that (a) the result will be ruinous to the person’s health, reputation, career, or whatever, and also (b) the thing they are fighting for is petty, foolish, silly, or otherwise unworthy of sacrifice.
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