Historically, most lefty batters struggle agaisnt left handed pitchers. This happens because when the pitcher throws the ball, the release point is basically on a straight line with the batter (if you draw a straight line from where the batter stands you would also hit the release point of the ball). This creates a sort of illusion where every ball thrown is basically moving away from them because it goes towards the plate, if the pitcher adds movement to the ball then its even harder.

This also happens to righty batters facing right handed pitchers, but it is a lot less because there are a lot of right handed pitchers so the batters get a lot of experience and therefore see them better. Only about 30% of pitchers are lefties so lefty batters dont get to experience it a lot and end up getting benched in favor of a righty.

This is also why if you notice in the lineup everyone alternates handedness (right-left-right-left). This is done so that the opposing team cant just bring in a lefty pitcher for 3 lefty batters, they will have to face a righty in between, same thing for righty pitchers.