Because of CO2. It's an acid. The water (and probably the CO2 as well) distributes the capsaicine (the chemical compound that tricks your body into feeling pain (hotness)) in your mouth instead of making it go away.

Does soda make spicy food worse?

Sure, it puts out real fires just fine, but when you drink it, it simply spreads out the spiciness in your mouth and makes matters worse. Oil and water don't mix. Drink carbonated drinks. Because sodas are water-based, you'll have the exact same problem if you take a swig of soda to cool down a burning tongue.

Why does soda make spicy things spicier?

More: Food

Researchers say milk works so well thanks to the protein casein, which overpowers capsaicin, the compound that causes a fiery kick. Sugary drinks work because capsaicin can be overwhelmed with sweetness.