This is how Tony learns of S.H.I.E.L.D.'s plan to weaponize a powerful alien artifact ... while somehow missing an even bigger threat. In Captain America's second solo outing, The Winter Soldier, we learn that S.H.I.E.L.D. has been eaten from the inside by a bunch of neo-Nazis named HYDRA. Think if the CIA was secretly run by the staff of Breitbart. The HYDRA infiltration isn't a recent development, either; they've been pulling the levers for 70 freaking years, intentionally creating wars and world chaos like terrible Civilization players.
So, uh, how did Stark and J.A.R.V.I.S. miss something like that? They dug deep enough to discover that S.H.I.E.L.D. was already into building superweapons, but somehow they missed the gigantic helicarriers intended to kill millions of people? You know, the ones that are almost entirely finished just a few months later? Come on, the only thing that could grab Tony Stark's attention faster than "flying airplane carriers that can also murder anyone on Earth" would be some Aunt May nudes. Which are probably there too.
And even if there wasn't a secret Nazi forum where HYDRA employees could complain about Jewish co-workers and share 4chan memes, surely there were some files that would raise suspicion. After all, the Winter Soldier has been assassinating people on behalf of HYDRA for decades -- including Tony's parents. The only reasonable explanation is that J.A.R.V.I.S. is himself a Nazi and was hoping HYDRA's special helicarrier project would eliminate the Avengers before he was found out. There's no way the next movie doesn't end with the Vision murdering everyone and saying "Hail HYDRA."