gas stove went out while cooking. Isn't this incredibly dangerous? ?

FIRST Forget the TV shows that show a gas stove gassing up a room.  That does not happen. It can't because the shut off relay is heat sensitive so it senses when there is a flame or not. No flame= no gas.(faster than you can blink).  The release of gas can only happen when you are back at the controls at IGNITION. That is the only time gas is released and it is being ignited at that moment.

.   meaning if the stove flame were to blow out. the gas shuts off automatically.  Works that way for the gas furnace and for the water heater too.(if they are natural gas or propane.)

. They thought of that when they invented the gas valve which is very old.  

Google it because I am not going to do that for you.(guessing the 20's or the 40's was the invention.

MacGyver can't even jimmy it open.  He won't.  He will use a propane tank and open that valve.  So much easier.

Buy an electric stove. {When the flame goes out a sensor (should!) shut off the gas. idk if you smelled raw gas, or partly burned gas.}  Go outside with a wrench and turn the gas off at the meter; then call the gas company.

I’d say avoid the situation where that would happen, and if your stove has a tendency to do this NEVER leave the kitchen while cooking.

It's dangerous to leave a gas flame unattended. Common sense.  Stay in the kitchen when the cooktop is in use, or at least, check it frequently. Don't let a pot boil over. Turn off the gas when this happens. Open a window for circulation. Turning the knob to the off position will not trigger the igniter.

i would hire someone to come check it out

Water boiled over and put out the flame.  You need to watch it closer in future boils.

i would get someone to check it out