Why didn't Jason know his own future?
Throughout the series, Jason is somewhat taken aback when he meets people whose names he is familiar with (like Medusa and Oedipus, for example), because he knows their stories and how their lives will turn out. So, it's a given that he (being from the future) has knowledge of classical mythology. Add to that the fact that he is told time after time that characters in Atlantis can't escape their destiny.
Given all this, why doesn't he remember his own story from mythology, and the really horrible way his life turns out? The Jason story is pretty famous, after all! Maybe the thought is too depressing, and he's hoping it was about another "Jason"? Heh, heh... I guess that it was too much to face; the latter part of his life was a complete disaster, very tragic---who wants to admit that things are fated to turn out so very badly?