From Longman Dictionary of Contemporary Englishall the more reason why/to do somethingall the more reason why/to do somethingspokenREASON used to say that what has just been mentioned is an additional reason for doing what you have suggested But surely that’s all the more reason to act quickly. → reason
Examples from the Corpus
all the more reason why/to do something• But that's all the more reason why we should go off this time with a car well filled, eh?• If some material is lost already, that is all the more reason to stop a lapse becoming a loophole.• That means there is all the more reason to oppose the willed destruction of old things.• That possibility is all the more reason to end the conflict soon.• This is all the more reason to find a more democratic way of deciding the state for the first primary. 