A furnace is probably the worst heating system you can have. First, the furnace has one of the shortest lifespans. If you are really on it, the furnace will live about 15 years. That is all you can get out of the furnace, a lousy fifteen years out of it. Second, the furnace is super dirty. The heater sucks in air, churns away and forces it back out of the vents. If you have a pet, the dander is getting sucked up. If you are not on it with air filter changes, the dust will get into the system and pollute your indoor air quality. What is doubly fun is that a dirty air filter could cause the whole heater to die. An air filter that costs a few bucks could cause your very expensive heater to totally break.
This leads into the next problem with the furnace. The heat exchanger could break on the furnace if it overheats. The heat exchanger costs as much as the whole furnace. Also, the heat exchanger when cracked, releases carbon monoxide into the home. This is an odorless, tasteless and colorless gas. It can poison you without you even realizing it. Yes, this terrible heating system can potentially kill you if it gets a little too hot. A microscopic crack can cause your whole family to be hospitalized. Last, the furnace requires so much work. Basically every season the heater needs to be looked it. It needs cleaning, oiling and tightening of parts all of the time. Expect frequent heating maintenance that costs a fortune.