"no hay de qué" is a short way to say: "no hay de qué agradecer". We make "agradecer" an implicit word here, whereas in English there's no way in implicit the "thank" word in the phrase "there's nothing to thank for"... actually it might be similar to the English phrase "it's nothing" as a shorter of the previous phrase, btw I wouldn't suggest you to try to find logic to"spanish sayings" in english language structure...