Because it's a chemical reaction: vinegar is an acid, baking soda is a base, and when they meet they release carbon dioxide gas — the fizz is thousands of tiny CO₂ bubbles escaping at once.
Every school volcano runs on this reaction. The "eruption" isn't the liquids pushing up — it's the gas. CO₂ forms faster than it can dissolve, bubbles race to the surface, and the foam rides them up and out. Add dish soap and the bubbles last longer, which is why volcanoes (and drain-cleaning videos) look so dramatic.
In an open cup, the gas escapes. Seal it in a bottle and the pressure climbs with nowhere to go — the container can rupture and spray the mix everywhere. That's why the rule with this pair is the same as our gallium rule: fun to watch, don't bottle it up and shake it.
Here's the part nobody mentions: once the fizzing stops, you're mostly left with salty water. The acid and base cancel each other out — that's literally what the reaction is. Each one is a decent cleaner on its own for certain jobs, but mixed together, the famous fizz is mostly show.
See the 23-second version:
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Fascinating facts you didn't know. Come learn with me — no pressure.
Sources: standard chemistry references for the acetic acid + sodium bicarbonate reaction (products: carbon dioxide, water, sodium acetate).