By the way, the expression (many say) comes from one of the animal fables of Aesop. That is, it would be the thought of the stag that fled from the dogs (to a cave), but...in the cave there was a lion (a famished lion certainly).
So, the stag was out of the frying-pan into the fire (as expressed by Aesop).http://mythfolklore.net/aesopica/vernonjones/243.htmhttps://www.bloomsbury-international.co ... -the-fire/
It´s worth noticing that it´s a lose-lose situation, even if one could reverse the situation: out of the fire directly into the frying pan!
But usually (by seeing the expression somewhere) we will have the knee-jerk reaction of thinking that the subject would be better off not jumping into the fire, as if he/she would have a choice! Or if he had not decided on jumping he would be better off...
Usually not deciding is already a decision, this is one of the cases that prove it well. Unfortunately for worse, sort of.