To make an already tense, angry, or unstable situation even worse.
Using the reference
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To add fuel to the fire means to intensify an argument, crisis, or emotional situation that is already heated.
The phrase describes a move that makes things worse instead of calming them down. That move might be a comment, a decision, a rumor, or even bad timing.
People use this idiom during conflicts, office disputes, family arguments, public controversies, and online pile-ons. It usually carries a warning that someone is escalating rather than resolving the problem.
You will also hear add fuel to the flames and fan the flames. They all point to escalation, though fan the flames usually emphasizes active encouragement.
This is a durable fire metaphor with a long history in English and earlier sources. The image is simple enough that it has stayed easy to understand across centuries.