TL;DR: Tell a story where you lost, committed properly, and either were proved wrong or handled being proved right without saying so. The trap is answering with a disguised victory. The signal being read is whether you can be overruled and still be useful, which is what makes someone safe to promote.
How to approach it
Pick a real loss where the stakes were genuine. Give the disagreement in one line, the argument you made and the evidence behind it, the decision, and then spend most of the answer on what you did next, because that is the part being scored.
A strong answer
Four beats.
The disagreement, stated fairly. Describe the other position as its holder would, not as a straw man. "The team wanted to ship on the managed service; I argued for self-hosting because our latency requirement was below what the managed tier committed to." If your description makes the other side sound obviously wrong, the interviewer concludes you never understood it, and everything after is discounted.
How you argued. Evidence, in the language of the decision. A benchmark, a cost model, a specific failure scenario with a probability. "I felt strongly" is not an argument. Say who you took it to and how far you escalated, because knowing when to escalate and when to stop is part of the skill.
How you committed. This is the beat that carries the answer. You lost, and then what? The good version is specific: you helped implement the thing you argued against, properly, and you did not relitigate it in later meetings. If you added a safeguard, say so, because instrumenting your own concern is a strong move: "I disagreed, and I added a dashboard for the metric I was worried about, so we would know early if I was right."
What happened. Both endings are good if handled well.
If you were wrong, say so plainly and explain what you had misunderstood. Describe how the result changed a later decision; that gives the interviewer evidence of learning beyond a general claim that you accept feedback.
If you were right, be careful. Describe what happened factually, what the safeguard caught, and how the team responded. Do not narrate vindication. A candidate who tells this story with relish is telling the interviewer what they will be like on a team that overrules them, which is not a story about good judgement.
The framing worth naming: disagree and commit is not agreeing under protest. It is arguing fully while the decision is open and then executing as if it were yours, because a team that half-executes a decision converts a defensible choice into a bad outcome and then cannot tell which it was.
What interviewers probe next
"What would you do differently?" Usually about the argument rather than the outcome: earlier, with better evidence, to a different audience, or written down instead of in a meeting.
"When would you escalate above your manager?" For unresolved material risks, explain the normal escalation path and its time limit. An active severe incident, prohibited action or urgent safety concern can require immediate escalation without exhausting every rung.
"What if you were asked to do something unsafe?" Different question entirely, and the answer is that commitment has a limit at safety, legality and ethics. Knowing that this is where the principle stops is the point.
Common mistakes
Telling a disguised win, where you lost the argument and were vindicated in a paragraph. Interviewers hear this constantly and score it as an inability to be wrong.
Choosing a trivial stake, which signals you have never been in a real disagreement.
Describing commitment as compliance. "I did what I was told" is not the same as executing well, and the difference is audible.