From what I read, when a RHP throws a curveball or a slider, that pitch will curve away from a RH Batter and into a LH Batter. And I also read that a ball curving into a hitter is harder for that hitter to handle than a ball curving away. That would mean that a RHP is more effective against LH Batters than he is with a RH Batter. And the same logic for LHPs. That is, LHPs curveballs/sliders curve into a RH Batter and away from a LH Batter. Therefore an advantage for the LHP over RH Batter.
But I have also read that RHPs have advantages over RH Batters and LHPs with LH Batters.
I’ve played baseball my whole life so far (I’m 18), I’d say that it has to do with vision of the ball on “normal” pitches. Pitches that don’t break are much easier to hit if the pitcher is of the oppisite hand from you, because the ball will be coming in from the other side of the plate, and it seems “less dangerous” to the batter if the ball is coming from the other side of the mound, making them more aggressive.