The last one in the majors was in 1989. There doesn't seem to be a real consensus on why exactly all catchers throw right handed, but I have a theory. It's because of a few things:
Most people are right handed. This is the largest pool of players (obviously)
If you're left handed, and can hit, you'll always find somewhere to play.
If you can't hit, next in line would be to become a pitcher because of the inherent value in LHP. Even if you aren't great, these guys still manage to get drafted. Lefty pitchers are a massive premium in baseball.
If you're right handed, and can hit, generally you'll find a position to play. If you can't hit, and you can't pitch, you're gonna be blocked by a lot of guys (due to being in a much larger pool of righties) unless you learn how to catch.
So basically it boils down to there being more righties than lefties, and catcher being the least desirable position to play
What do you think?