Leaving a pot on the stove with nothing in it generally won't set your house on fire. However, if there is residual oil, grease, or any other flammable substances in the pot, and the stove is left on at a high temperature for an extended period, it can lead to a fire hazard. The heat can cause the flammable residues to ignite and spread, potentially causing a fire.
Metal itself is not flammable, as you correctly pointed out. However, metal pots and pans conduct heat very effectively. When a pot is left on a hot stove for too long, it can become extremely hot. If there are other flammable materials nearby, such as kitchen towels, wooden utensils, or even nearby curtains, the intense heat from the metal pot can transfer to those items and ignite them.
Additionally, if the pot is left on a gas stove with the burner turned on but no pot contents to absorb the heat, the heat can build up and damage the pot itself, possibly leading to a fire hazard in extreme cases.
To prevent such incidents, it's essential to always be cautious in the kitchen. Make sure to turn off the stove when not in use, keep the area around the stove clear of flammable materials, and regularly clean pots and pans to prevent the buildup of flammable residues. Using a timer or setting a reminder when cooking can also help prevent forgetting about food on the stove. Always prioritize safety to avoid potential fire hazards.