Game answer: Equiping GFs make people lose their long term memories. Squall, Quistis, Zell and Selphie don't remember anything because they used GFs while growing up in order to train. Irvine did not, and thus remembers everything from when they are children. He doesn't say anything until disk 2 because "no one else remembered".

Real Answer: Square needed to work out a plausible reason as to why Squall and co. wouldn't remember events from 10 years ago. When they couldn't think of one, they made up some stupid crap about GFs making people forget and put one line in the database in a half-assed attempt at foreshadowing. The result is the most ridiculous, confused, unnatural, deus ex machina plot twist to ever grace the series.

Hope that answers your question.