Meanings
An allusion to the military practice of capturing/holding a hill (high ground), no matter the cost or (lack of) benefit, as in the Battle of Hamburger Hill or Last Stand Hill.
How to pronounce "hill to die on":
AU
An issue to pursue with wholehearted conviction and/or single-minded focus, with little or no regard to the cost.
Example Sentences
1
I understand you have a different opinion, but this is not a hill to die on. Let's find a compromise.
2
The team leader wouldn't budge on the project deadline, making it a hill to die on for everyone else in the group.
3
The manager decided to make the new dress code policy a hill to die on, even though most employees disagreed with it.
4
He refused to compromise on the terms of the contract, turning it into a hill to die on for the negotiations.