Question:Why is preparing charcoal forbidden even though charcoal can be used for cooking and warming oneself near the fire? How is this different from chopping wood which is permitted to chop wood which is used in a similar manner? Why does the fact that charcoal can be used for a non-permitted purpose negate the possibility of using the rule of me-toch?
The Chachamim did not prohibit making coals because one might use it for heating a steamhouse or to forge gold (for the Isur to make coal existed before the enactment not to sweat in a steamhouse). The Isur of making coal is because of Tikun Kli, since the coal needs to be properly made. It is not like wood used for fuel, because wood is used in its present form and do not need any Tikun in order to use it as fuel. This is also clear from Rashi on the Mishnah.