Do you know the story about how Whitey Ford started his career?
Casey Stengel was an interesting manager. He pioneered several practices that have become baseball institutions like the lefty/righty platoon.
But he handled Whitey Ford oddly when the blonde lefty joined the staff.
Stengel already had a veteran staff including Superchief Allie Reynolds, Johnny Sain, and Eddie Lopat. So he used Ford like a wild card, pitching him in big games against the other aces rather than simply letting him pitch every 4th day. For the first 8 seasons of Ford's career, he averaged only 28 starts and 205 IP in a 4 man rotation.
After losing the 1960 World Series in a 7th game walkoff to the Pirates, Casey was forced out.
Ralph Houk took the helm of the '61 club and asked Ford if his arm bothered him and that's why Casey used him that way. Ford said no. For the next 5 seasons he averaged 37 starts and 260 inning per year.
Sometimes managers get too cute, too smart for the best interest of the team.
Brett Gardner has hit .264/.335/.373 against righties in 193 ABs. He's hit .291/.381/.400 against lefties.
This has small sample size stamped all over it, so I'm not arguing that Gardner might actually hit lefties better than he hits righties (though he's see fewer changeups). My point is that we don't know, and that Gardner's main weapons, his plate discipline and his speed, are uneffected by the handedness of the pitcher.
Maybe Joe G. needs to trust his player's talent just a little bit more. Gardner can't look more lost at the plate that Swisher does right now. And maybe putting the defensively gifted center fielder back in the lineup would be the best thing for the team.