This may seem like a silly question, but it will help settle a huge disagreement in my house. One of us, on occasion, accidentally sets the heat to "emergency heat" at night. The other one of us yells and fusses that the first one is going to burn the house down by doing so. I have not found any information that indicates that the "emergency heat" setting is dangerous or a fire hazard. If so, one could argue, it would probably not be available. Why then, would there be such a fuss over emergency heat getting accidentally set? Is there some danger that is being overlooked?

It will not burn the house down but it will cost more on the utility bill.

Only thing that will burn is your money

This may seem like a silly question, but it will help settle a huge disagreement in my house. One of us, on occasion, accidentally sets the heat to "emergency heat" at night. The other one of us yells and fusses that the first one is going to burn the house down by doing so. I have not found any information that indicates that the "emergency heat" setting is dangerous or a fire hazard. If so, one could argue, it would probably not be available. Why then, would there be such a fuss over emergency heat getting accidentally set? Is there some danger that is being overlooked?
Its April, why do you need to run the emergency heat!

The Emergency Heat feature uses a resistance heating coil similar to that on an electric stove. Electricity flows through a resistance wire and becomes hot. Air passes over the coil and is heated by the coil.

Typically, emergency heat is used with a heat pump to provide extra heat when the temperature becomes too low for the heat pump to extract much useful heat from the outside air. In other words, you lose heat through your windows, air leaks, and poor insulation.

Heat pumps also become less efficient as the temperature becomes colder.

You should not need to use the emergency heat feature unless it is cold outside, say less than 32°F. You would be better served by purchasing a oil filled electric heater for your bedroom. Stay away from ceramic heaters and other electric heaters. They are just too unsafe.

Best of luck.