Cory is a very technical goaltender. He stops pucks by being in the right position more often than not. It's basically how most butterfly goalies are nowadays.
He lacks an advanced anticipatory component where he can read plays to the degree that he can cheat. He does this.. as every NHL goalie does.. but it lags significantly behind his technical abilities.
He's also not a very aggressive goalie. So you have the shootout where it's basically the shooter being able to dictate the play. Not being aggressive allows the shooter to take his time and walk right in. He doesn't anticipate the shooter very well so it's really just too easy.
It's just not something he's very good at right now. You see goalies like Marty excel in it because he reads into the play. He guesses.. way more often right than not. He plays aggressive and forces the shooter to change up his plan, leading to mistakes or pressure forcing the shooter wide.
First step is just being more aggressive in the shootout. Play farther out of the crease. Learn how to employ a pokecheck (something I can't recall Schneider ever doing) effectively. End of the day, it's a skills competition and I really don't care too much about it... but these are valuable points.