Here's why:

* It's a salt: Barium chloride is an ionic compound, not a combustible material like wood or fuel. It doesn't have the chemical structure to undergo combustion.

* No oxidation reaction: Burning requires a rapid reaction with oxygen (oxidation), releasing heat and light. Barium chloride doesn't react with oxygen in this way.

While barium chloride itself doesn't burn, it can be used to produce a green flame in fireworks. This is because the barium ions in the compound emit green light when heated to a high temperature.

However, it's important to note that handling barium chloride requires caution as it's toxic.