Fats are basically glycerol esters. (1,2,3-propanetriol) Where long chain carboxylic acids or other compounds are attached by ester bonds to the glycerol oxygens. Esters are electrophilies, and do undergo nucleophilic attack to form the carboxylate anion and alcohol. So caustic substances hydrolyse the fats and lipids in your cells and to immense damage to the structure. Acids are similar.