First of all, it damages the nature by consuming wood.
It also causes Air pollution and releases Carbon Dioxide and Particulate matter into the Atmosphere.
Mostly, in burning firewood, incomplete combustion takes place and less energy is obtained. Thus it is less efficient.
Moreover, it deposits a layer of Carbon Black on the underneath of Utensils, which makes work of cleaning difficult.
Also, there is no control over the temperature of the flame obtained by burning firewood.
You need an open space for burning firewood. Then you need to collect firewood, prepare the stand, ignite the flame (mostly by adding kerosene) and sit beside it to see that the flame doesn't go out. You need to keep an eye on the flame and keep adding firewood.
Further, you can be accidentally burnt by the uncontrollable flame. It can cause fire in the house or on your clothes.
Also, you can't rely on it in Monsoon!
You don't need to face any of these hassles while using LPG or modern cooking appliances like Induction Cook-top and Microwave Oven. So, burning of firewood in traditional Chulhas is considered disadvantageous.