Overwhelming exception

Name of fallacy Overwhelming exception fallacy
Type Inductive Argument, Informal Argument
Description It is a generalization which is accurate, but comes with one or more qualifications which eliminate so many cases that what remains is much less impressive than the initial statement might have led one to assume
Example "Our foreign policy has always helped other countries, except of course when it is against our National Interest..." (The false implication is that our foreign policy always helps other countries).
Treatment Dealt with by restating the generalization to show the significance.