>>719839494
Him holding back information about the Final Aeon is apparently part of his plan. The scene that plays as he encourages the party to defy Yunalesca is the most emotion and energy he shows in the entire game, seemingly the moment he has been preparing for. He is apparently of the opinion that the shock of the revelation will be helpful in persuading them to act.
If we go with this explanation, then he also can't tell Tidus the full truth about his father because it would require revealing the truth about the Final Aeon. It's also not clear that Auron himself fully understands what happened to Jecht. As I recall, Jecht and Braska go off to fight Sin alone, and exactly what happens to the Final Aeon after defeating Sin is not fully explained (e.g. why does it take Yu Yevon so many years to assert control and re-establish Sin?).
An alternative explanation is that Auron is ashamed of his past, especially in admitting it to Jecht's son, and his decision to not inform the party should be interpreted as a personal failing.