You'll be furious that your friend didn't bake the cupcakes she promised for your bake sale — until you learn the extenuating circumstances: her dog climbed onto her kitchen counter and ate all the cupcake batter. Extenuating means "making forgivable."
The adjective extenuating is unusual because it's almost always used with the word circumstances; the phrase extenuating circumstances describes the specific reasons that excuse or justify someone's actions. The phrase became popular in the 1840s, and is even used in law to lessen punishment for crimes, but before that extenuating meant "lessening or making small." The Latin word for "thin," tenuis, combined with ex, means "to make thin", or to dilute a person's guilt because of a good excuse.